Copyright  1921, 
By  FREDERICK  P.  SPALDING 


PRESS  OF 

BRAUNWORTH   &   CO. 

BOOK    MANUFACTURERS 

BROOKLYN,   N.  Y. 


PREFACE 


THIS  book  is  designed  to  present,  in  a  brief  and  systematic  man- 
ner, the  fundamental  principles  involved  in  the  design  and  construc- 
tion of  masonry  structures. 

The  term  Masonry  has  been  construed  to  include  concrete,  and 
the  field  covered  by  the  title  is  a  very  wide  one.  It  has  therefore 
been  necessary  to  select  for  discussion  those  types  which  seem  most 
adequately  to  illustrate  the  principles,  and  no  attempt  has  been  made 
to  cover  fully  the  details  of  all  classes  of  masonry  structures.  The 
purpose  has  been  to  provide  an  introduction  to  the  subject,  which  may 
later  be  followed  by  intensive  study  in  more  detailed  works  upon  the 
various  branches.  This  gives  a  general  view  of  the  subject  as  a  whole, 
and  is  the  natural  method  of  approach. 

The  Author  has  derived  much  assistance  from  a  number  of  books 
which  deal  more  fully  with  various  portions  of  the  subject.  These 
are  mentioned  at  the  ends  of  articles  or  chapters  to  which  they 
specially  relate.  They  should  be  studied  by  students  desiring  a 
more  complete  presentation  of  the  subject. 

Special  acknowledgment  is  also  due  to  Professors  A.  Lincoln 
Hyde  and  Guy  D.  Newton  of  the  University  of  Missouri  for  reading 
and  criticising  portions  of  the  manuscript  and  for  assistance  in  pre- 
paring the  illustrations. 

F.  P.  SPALDING. 
COLUMBIA,  MISSOURI, 
September,  1920. 


436264 


iii 


CONTENTS 


CHAPTER  I 
DEVELOPMENT  OF  MASONRY  CONSTRUCTION 

PAGE 

ART  1. — INTRODUCTION 1 

1.  Definition;  2.  Uses  of  Masonry. 

ART.  2 — EARLY  HISTORY 3 

3.  Ancient  Masonry;  4.  Roman  and  Medieval. 

ART.  3. — RECENT  DEVELOPMENTS 5 

5.  The  Cement  Industry;  6.  Reinforced  Concrete. 

CHAPTER  II 
CEMENTING  MATERIALS 

ART.  4. — LIME 9 

7.  Classification;  8.  Common  Lime;  9.  Hydraulic  Lime;  10.  Hydrated 
Lime;  11.  Specifications. 

ART.  5. — HYDRAULIC  CEMENT 16 

12.  Setting  and  Hardening;  13.  Portland;  14.  Natural;  15.  Puzzolan; 
16.  Sand  Cement;   17.  Soundness;   18.  Chemistry  of  Cement. 

ART.  6. — SPECIFICATIONS  AND  TESTS  FOR  CEMENT 26 

19.  Specifications;    20.  Purpose  of  Tests;    21.  Compressive  Strength; 

22.  Special  Tests. 

ART.  7. — SAND  FOR  MORTAR 31 

23.  Quality;     24.  Tests;     25.  Mechanical    Analysis;     26.  Voids;     27. 
Specific    Gravity;     28.  Density;     29.  Strength    Test;     30.  Washing; 

31.  Specifications. 

ART.  8. — CEMENT  MORTAR 39 

32.  Proportioning;     33.  Mixing;     34.  Yield;     35.  Mixtures    of   Lime 
with  Cement;  36.  Strength. 

ART.  9. — GYPSUM  PLASTERS 48 

37.  Classification;  38.  Properties  and  Uses. 

v 


vi  CONTENTS 

CHAPTER  III 
STONE   MASONRY 

PAGE 

ART.  10. — BUILDING  STONE 51 

39.  Qualities;  40.  Classification;  41.  Strength;  42.  Durability. 

ART.  11. — STONE  CUTTING 62 

43.  Tools;  44.  Methods  of  Finishing;  45.  Machinery. 

ART.  12. — WALLS  OF  STONE  MASONRY 70 

46.  Classification;  47.  Parts  of  Wall;  48.  Stonework;  49.  Trimmings; 

50.  Specifications. 

ART.  13. — STRENGTH  OF  STONE  MASONRY 78 

51.  Compressive;     52.  Capstones    and    Templets;     53.  Lintels    and 
Corbels. 

ART.  14. — MEASUREMENT  AND  COST 82 

54.  Measurements;  55.  Cost. 

CHAPTER  IV 
BRICK  AND  BLOCK  MASONRY 

ART.  15. — BUILDING  BRICKS 85 

56.  Clay  and  Shale;  57.  Sand  Lime;  58.  Cement;  59.  Tests. 

ART.  16. — BRICK  MASONRY 93 

60.  Joints;    61.  Bond;    62.  Strength;  63.  Efflorescence;  64.  Measure- 
ment and  Cost. 

ART.  17. — TERRA  COTTA  CONSTRUCTION 102 

65.  Structural    Tiling;      66.  Block    Construction;      67.  Architectural 
Terra  Cotta. 

ART.  18. — GYPSUM  AND  CEMENT  CONCRETE  BLOCKS 107 

68.  Gypsum  Wall  Blocks;    69.  Roof  and  Floor  Blocks;    70.  Hollow 
Concrete  Blocks. 

CHAPTER  V 
PLAIN  CONCRETE 

ART.  19. — AGGREGATES  FOR  CONCRETE 110 

71.  Materials;  72.  Tests  for  Coarse  Aggregates. 

ART.  20. — PROPORTIONING  CONCRETE 116 

73.  Arbitrary;    74.  Voids;    75.  Analysis  Curves;    76.  Trial;    77.  Fine- 
ness Modulus  and  Surface  Area;  78.  Yield. 


CONTENTS  vii 

PAGE 

ART.  21. — MIXING  CONCRETE ..  c 125 

79.  Preparing  Materials;  80.  Hand  Mixing;  81.  Machine. 

ART.  22. — PLACING  CONCRETE 129 

82.  Transporting;      83.  Depositing;      84.  Freezing;      85.  Contraction 
Joints;  86.  Finishing  Surfaces. 

ART.  23. — WATERTIGHT  CONCRETE 136 

87.  Permeability;  88.  Integral  Waterproofing;  89.  Exterior  Coatings. 

ART.  24. — DURABILITY  OF  CONCRETE 140 

90.  Destructive    Agencies;     91.  Sea    Water;     92.  Alkalies;     93.  Fire 
Resistance. 

ART.  25. — STRENGTH  OF  PLAIN  CONCRETE 144 

94.  Compression;  95.  Tests;  96.  Tension  and  Transverse. 

ART.  26. — COST  OF  CONCRETE  WORK 149 

97.  Materials;  98.  Labor;  99.  Total  Costs. 

CHAPTER  VI 
REINFORCED  CONCRETE 

ART.  27. — GENERAL  PRINCIPLES 153 

100.  Object  of  Reinforcement;  101.  Bond  Strength;  102.  Reinforcing 
Steel;  103.  Modulus  of  Elasticity;  104.  Reinforced  Concrete  in  Tension. 

ART.  28. — RECTANGULAR  BEAMS  WITH  TENSION  REINFORCEMENT 158 

105.  Flexure    Formulas;      106.  Tables;      107.  Shear;      108.  Diagonal 
Tension;  109.  Bond;  110.  Design. 

ART.  29. — T-BEAMS  WITH  TENSION  REINFORCEMENT 178 

111.  Flexure  Formulas;  112.  Shear  and  Bond;  113.  Diagrams. 
ART.  30. — BEAMS  REINFORCED  FOR  COMPRESSION 186 

114.  Flexure  Formulas;  115.  Tables  and  Examples. 
ART.  31. — SLAB  AND  BEAM  DESIGN 194 

116.  Bending  Moments  and  Shears;  117.  Loadings;  118.  Design. 
ART.  32. — CONCRETE  COLUMNS 206 

119.  Plain    Concrete    Columns;      120.  Longitudinal    Reinforcement; 

121.  Hooped  Reinforcement;  122.  Eccentric  Loads. 

CHAPTER  VII 
RETAINING  WALLS 

ART.  33. — PRESSURE  OF  EARTH  AGAINST  A  WALL 214 

123.  Theories;  124.  Computations;  125.  Graphical  Method. 


viii  CONTENTS 

PAGE 

ART.  3*.-   SOLID  MASONRY  WALLS 223 

126.  Stability;  127.  Empirical  Design;  128.  Design  Using  Formulas. 

ART.  35. — REINFORCED  CONCRETE  WALLS 229 

129.  Types;   130.  Cantilever  Walls;   131.  Counterforted  Walls. 

ART.  36. — CONSTRUCTION  OF  RETAINING  WALLS 244 

132.  Foundations;  133.  Drainage  and  Back-filling;  134.  Gravity  Walls. 

CHAPTER  VIII 
MASONRY  DAMS 

ART.  37. — GRAVITY  DAMS 247 

135.  Stability;    136.  Graphical  Analysis;   137.  Design  of  Profile;    138. 
Diagonal  Compressions;   139.  Horizontal  Tension;   140.  Uplift. 

ART.  38. — DAMS  CURVED  IN  PLAN 258 

141.  Curved  Gravity  Dams;    142.  Arch  Dams;    143.  Multiple  Arch 
Dams. 

ART.  39.— REINFORCED  CONCRETE  DAMS 266 

144.  Arch  Dams;  145.  Flat  Slab  and  Buttress  Dams. 

ART.  40. — CONSTRUCTION  OF  MASONRY  DAMS 268 

146.  Foundations;  147.  Masonry;  148.  Qxe&ow  Dams. 


CHAPTER  IX 
SLAB  AND  GIRDER  BRIDGES 

ART.  41. — LOADINGS  FOR  SHORT  BRIDGES 271 

149.  Highway  Bridges;   150.    Distribution  of  Concentrated  Loads;   151. 
Railway  Bridges. 

ART.  42. — DESIGN  OF  BEAM  BRIDGES 273 

152.  Slab  Bridges;  153.    T-Beam  Bridges;  154.  Girder  Bridges. 

CHAPTER  X 
MASONRY  ARCHES 

ART.  43. — VOUSSOIR  ARCHES 282 

155.  Definitions;  156.  Stability. 

ART.  44. — LOADS  FOR  MASONRY  ARCHES 286 

157.  Highway  Bridges;  158.  Railway  Bridges;  159.  Dead  Loads. 


CONTENTS  ix 

PAGE 

ART.  45. — DESIGN  OF  Voussom  ARCHES 289 

160.  Methods;   161.  Thickness  of  Arch;  162.  Stability. 

ART.  46. — THE  ELASTIC  ARCH 295 

163.  Analysis;   164.  Temperature;  165.  Direct  Thrust. 

ART.  47. — DESIGN  OF  REINFORCED  CONCRETE  ARCH  .  .  . . : 300 

166.  Selection   of   Dimensions;     167.  Division   of    Arch   Ring;     168. 
Analysis;   169.  Stresses. 

ART.  48. — TYPE  OF  CONCRETE  ARCHES 309 

170.  Arrangement    of    Spandrels;     171.  Methods    of    Reinforcement; 
172.  Hinged  Arches;   173.  Unsymmetrical  Arches;   174.     Elastic  Piers. 

ART.  49. — OTHER  METHODS  OF  ANALYSIS 314 

175.  Influence  Lines.     176.  Arbitrary  Divisions. 

CHAPTER  XI 
CULVERTS  AND   CONDUITS 

ART.  50. — CULVERTS 321 

177.  Types;  178.    Area  of  Waterway;  179.    Pipe  Culverts;  180.    Box 
Culverts;  181.    Arch  Culverts. 

ART.  51. — CONDUITS 332 

182.  Types;  183.  Gravity  Conduits;  184.     Pressure. 

CHAPTER  XII 
FOUNDATIONS 

ART.  52. — FOUNDATION  MATERIALS 342 

185.  Examination  of  Soil;  186.  Bearing  Capacity;  187.    Tests  of  Bear- 
ing Capacity. 

ART.  53. — SPREAD  FOUNDATIONS 347 

188.  Distribution  of  Loads;    189.  Masonry  Footings;    190.  Grillage; 

191.  Reinforced  Concrete. 

ART.  54. — PILE  FOUNDATIONS 358 

192.  Classification;    193.  Pile  Drivers;    194.  Timber  Piles;    195.  Bear- 
ing Power;  196.  Concrete  Piles;   197.  Sheet  piling. 

ART.  55. — COFFERDAMS 373 

198.  Types;  199.  Sheet  Pile;  200.  Crib. 

ART.  56. — Box  AND  OPEN  CAISSONS 376 

201.  Box  Caissons;    202.  Types  of  Open  Caissons;    203.  Single-wall 
Timber;  204.  Cylinder;  205.  Dredging  through  Wells. 


X  CONTENTS 

PAGE 

ART.  57. — PNEUMATIC  CAISSONS. 387 

206.  Compressed  Air;   207.  Construction;   208.  Sinking;   209.  Physio- 
logical Effect. 

ART.  58. — BRIDGE  PIERS  AND  ABUTMENTS 393 

210.  Locations   and   Dimensions;    211.  Stability;    212.  Construction; 
213.  Types  of  Abutments. 


MASONRY  STRUCTURES 


CHAPTER  I 
DEVELOPMENT  OF  MASONRY  CONSTRUCTION 

ART.   1.     INTRODUCTION 

1.  Definition. — The  term  masonry  in  its  original  significance 
means  "  a  construction  of  dressed  or  fitted  stones  and  mortar." 
It  is  thus  properly  limited  to  stone  masonry.  Custom  has,  however, 
extended  the  use  of  the  term  to  cover  any  construction  composed  of 
pieces  of  inorganic  non-metallic  material  fitted  together  into  a  mono- 
lithic block.  This  includes  all  structural  work  in  stone,  brick,  and 
tile,  as  well  as  concrete  construction. 

The  word  brick  was  formerly  used  to  designate  a  small  block  of 
burned  clay.  Similar  blocks  of  other  materials  have  recently  come 
into  use,  and  we  now  have  several  kinds  of  bricks;  as  clay  brick, 
sand-lime  brick,  cement  brick,  etc.  Glazed  and  other  ornamental 
and  surfacing  tiles  are  commonly  employed,  while  hollow  tiles  of 
various  kinds  are  rapidly  coming  into  use.  All  construction  formed 
of  bricks  or  tiles  cemented  together  may  be  classed  as  brick  masonry. 

The  term  stone  masonry  is  used  to  designate  any  work  in  which 
stones  are  fitted  and  cemented  together  so  as  to  form  a  structure. 
Stone  masonry  is  further  subdivided  into  rubble  masonry,  squared- 
stone  masonry,  and  ashlar  or  cut-stone  masonry. 

Concrete  is  ordinarily  formed  by  mixing  broken  stone  or  gravel 
with  cement  mortar  to  a  mobile  condition  and  placing  it  in  forms  in 
the  position  in  which  it  is  to  be  used.  It  is  then  left  to  harden  and 
forms  a  monolithic  block. 

Ordinary  concrete  cannot  be  economically  employed  where  tensile 
stresses  are  developed  in  the  structure  on  account  of  the  low  tensile 
resistance  of  the  concrete.  It  is  therefore  common,  when  it  is  desired 
to  use  concrete  in  such  situations,  to  embed  steel  rods  in  the  con- 


2  DEVELOPMENT  OF  MASONRY  CONSTRUCTION 

crete  to  take  the  tensile  stresses,  leaving  the  concrete  to  carry  com- 
pression only.  This  construction  is  known  as  reinforced  concrete. 

2.  Uses  of  Masonry. — Masonry  in  some  form  is  now  used  in 
nearly  all  kinds  of  engineering  and  architectural  construction.  The 
selection  of  the  type  of  masonry  to  be  used  in  any  particular  structure 
is  ordinarily  largely  a  matter  of  cost,  the  latter  factor  depending 
upon  the  suitability  of  the  construction  to  the  use  to  which  it  is  to  be 
put,  and  the  availability  and  costs  of  the  necessary  materials  and 
labor.  These  factors  are  subject  to  local  variation  and  need  to  be 
considered  in  each  instance. 

Brick  masonry  is  largely  used  in  the  construction  of  buildings, 
being  usually  cheaper  than  stone,  and  when  of  good  quality  showing 
both  strength  and  durability.  Very  pleasing  architectural  effects 
are  readily  obtained  by  proper  selection  and  arrangement  of  materials 
in  brickwork.  Brick  masonry  is  frequently  used  in  the  construction 
of  large  sewers  and  in  the  arch  ring  of  small  arched  bridges,  and  is 
readily  adapted  to  such  uses,  but  is  gradually  giving  way  to  concrete. 

Hollow-tile  construction  is  being  quite  commonly  applied  in 
building  operations,  and  is  replacing  ordinary  brickwork  in  many 
instances.  It  is  sometimes  faced  with  brick  in  exterior  walls,  and 
is  used  for  partitions  and  in  solid  floor  construction  on  account  of  its 
lightness  and  low  cost. 

Stone  masonry  is  largely  used  in  architectural  construction, 
where  the  appearance  and  permanence  of  the  structure  are  of  special 
importance.  It  is  almost  universally  employed  in  monumental 
construction,  being  at  once  the  most  durable  material  known  to  man 
and  the  one  capable  of  producing  the  most  imposing  and  most  beau- 
tiful effect. 

Many  engineering  structures  such  as  retaining  walls,  bridge  piers, 
and  abutments  and  arch  bridges  are  often  constructed  of  stone 
masonry,  or  are  faced  with  stone.  Concrete  is,  however,  gradually 
replacing  stone  masonry  for  such  work  on  account  of  lower  cost  and 
facility  of  construction,  except  where  facing  of  stone  is  used  for 
appearance  or  durability. 

Concrete  is  almost  universally  employed  in  foundations,  having 
replaced  stone  masonry  for  this  purpose.  In  the  construction  of 
tunnels,  subways,  and  other  underground  work,  it  is  usually  the 
cheapest  and  most  convenient  material.  In  heavy  masonry,  such 
as  retaining  walls,  dams,  piers,  and  abutments,  concrete  is  com- 
monly used,  alone  or  with  a  facing  of  stone  masonry. 

The  use  of  reinforcement  makes  it  possible  to  apply  concrete  in 
many  types  of  construction  to  which  masonry  has  heretofore  been 


EARLY  HISTORY  3 

inapplicable.  For  short-span  bridges  reinforced  concrete  is  rapidly 
replacing  wood  and  steel,  and,  on  account  of  its  durability,  is  a  much 
more  economical  material  for  such  use.  Reinforced  concrete  is 
extensively  used  in  fireproof  building  construction  for  floors,  beams, 
and  columns,  and  is  frequently  used  in  connection  with  hollow  tile 
for  this  purpose.  It  is  sometimes  used  for  the  walls  of  buildings 
but  is  apt  to  be  more  expensive  than  brick,  on  account  of  the  forms 
necessary  in  such  work. 

ART.   2.     EARLY  HISTORY 

3.  Ancient  Masonry. — The  art  of  masonry  construction  dates 
from  the  earliest  records  of  authentic  history.  The  most  fruitful 
source  from  which  to  obtain  a  knowledge  of  the  history  of  the  more 
ancient  peoples  is  in  a  study  of  the  remains  of  their  masonry  struc- 
tures. 

The  earliest  important  constructions  of  which  we  have  any 
remains  are  probably  those  of  Chaldea  and  Assyria,  with  which 
the  great  constructions  of  Egypt  may  be  classed.  The  dates  of  few 
of  them  are  known  with  accuracy.  The  earliest  of  the  Chaldean 
remains  are  supposed  to  date  from  about  2500  B.C.  Alongside 
of  these  are  the  remains  of  the  second  Babylonian  Empire,  founded 
about  600  B.C.  Stone  and  timber  were  lacking  in  Chaldea,  and  hence 
the  natural  development  of  their  primitive  construction  was  toward 
the  use  of  brick.  In  the  earlier  and  more  crude  structures,  sun- 
dried  brick  of  rough  form  were  used;  later,  hard-burned  bricks 
were  employed.  In  some  of  the  early  buildings  both  classes  were 
used,  the  burned  bricks  being  employed  as  facing  to  protect  the 
sun-dried  from  the  weather. 

The  burned  bricks  of  the  earliest  times  are  still  found  to  be 
sound  and  hard,  and  many  of  the  sun-dried  still  keep  their  shapes. 
These  bricks  were  of  square,  flat  form,  the  burned  ones  varying 
from  11  to  13  inches  square  and  2J  to  3  inches  thick;  the  sun-dried 
were  somewhat  larger. 

According  to  Professor  Rawlinson,  the  cementing  material  in 
some  of  the  early  Chaldean  structures  was  either  a  coarse  clay, 
sometimes  mixed  with  straw,  or  a  bitumen  of  good  quality  which 
still  unites  the  bricks  so  firmly  that  they  can  with  difficulty  be 
separated. 

In  the  later  Babylonian  construction  the  character  of  the 
materials  shows  improvement,  and  elaborate  ornamentation  is 
introduced.  Ornamentation  was  accomplished  by  enameling  and 


4  DEVELOPMENT  OF   MASONRY  CONSTRUCTION 

carving  the  bricks  and  by  the  use  of  colors.  Ordinary  lime  mortar 
was  used. 

Assyria,  unlike  Chaldea,  had  plenty  of  stone.  The  type  of 
construction  used  by  the  Assyrians,  however,  was  probably  derived 
from  that  of  the  Chaldeans.  Brick  was  the  principal  material 
employed,  although  frequently  stone  was  used  to  face  the  brick 
walls,  and  sculptures  were  freely  used.  The  great  halls  of  their 
palaces  were  ornamented  with  sculptures;  the  entire  walls  in  some 
cases  to  a  height  of  10  or  12  feet  were  covered  with  figures  in  relief, 
representing  scenes  from  life,  and  usually  commemorating  the  great- 
ness of  the  monarch  for  whom  they  were  erected. 

The  arch  was  used  by  the  Assyrians  to  a  limited  extent  for  nar- 
row openings,  the  arches  being  of  brick,  which  were  made  narrower 
at  one  end  than  the  other,  in  order  to  fit  in  the  arch. 

The  art  of  construction  in  Egypt  was  much  more  advanced  than 
in  Assyria  and  Babylonia  and  was  probably  of  an  earlier  date.  The 
ancient  Egyptians  were  very  skillful  in  working  stone.  Their  tem- 
ples were  built  of  large  blocks  of  stone,  well  squared,  and  laid  so  that 
the  joints  are  scarcely  visible.  They  quarried  granite  and  trans- 
ported large  blocks  for  long  distances.  They  also  cut  and  polished 
granite. 

The  great  pyramid  has  a  base  of  764  feet  square  and  is  approxi- 
mately 486  feet  high,  and  is  built  in  courses,  of  great  blocks  of  lime- 
stone, from  2  to  5  feet  thick  and  as  much  as  30  feet  in  length.  The 
early  Egyptian  masonry  is  remarkable  both  on  account  of  the  great 
size  of  the  materials  and  the  exactness  with  which  they  are  fitted 
together,  no  mortar  being  employed. 

In  Greece  and  Italy  remains  are  found  of  Cyclopean  masonry 
built  of  stones  of  large  size  and  carefully  adjusted  joints.  The  walls 
of  Mycenae  were  built  of  irregular  blocks  of  great  size,  the  spaces 
being  filled  with  smaller  stones. 

Greek  Masonry. — The  masonry  of  the  Greeks  was  arranged  in 
courses  and  the  joints  carefully  fitted  and  equal  to  the  best  Egyptian 
workmanship.  The  carving  of  artistic  forms  was  here  for  the  first 
time  developed  to  a  high  degree  of  excellence. 

The  Egyptians  had  used  the  system  of  the  column  and  entab- 
lature in  their  temples.  The  Greeks  introduced  the  pediment,  and 
improved  the  artistic  design  of  the  buildings,  bringing  the  propor- 
tioning and  ornamentation  of  such  structures  to  a  most  wonderful 
perfection. 

4.  Roman  and  Medieval  Construction. — In  the  system  of  con- 
struction developed  by  the  Romans  the  walls  were  built  of  coarse 


RECENT  DEVELOPMENTS  3 

concrete  or  rough  cemented  rubble,  and  were  usually  faced  with 
brick  or  marble.  Sometimes,  in  less  important  construction,  small 
blocks  of  tufa,  set  irregularly,  formed  the  surface  of  the  walls,  which 
were  stuccoed  on  their  interior  surfaces. 

The  art  of  building  was  greatly  developed  during  the  Roman 
period.  The  introduction  of  the  arch  changed  the  whole  system 
of  construction.  In  the  Romanesque  architecture,  the  circular  arch 
was  the  principal  feature,  the  structures  consisting  mainly  of  heavy 
walls  supporting  semicircular  arched  roofs.  Roman  arches  were 
constructed  of  cut  stone,  brick,  or  concrete. 

The  introduction  of  the  pointed  arch,  and  later  of  the  use  of 
arched  ribs  with  piers  and  buttresses  to  transmit  the  loads  to  the 
foundations,  marks  another  advance  in  the  art  of  construction.  This 
made  possible  a  disposition  of  the  materials  of  the  structures  to 
better  advantage,  and  led  to  more  economical  construction. 

During  medieval  times  the  use  of  stone  masonry  was  brought 
to  a  high  state  of  perfection.  Random  ashlar  or  rubble  was  com- 
monly used  in  buildings  in  preference  to  coursed  ashlar.  Beautiful 
and  imposing  effects  were  attained  by  the  use  of  materials  of  rather 
small  size,  and  great  skill  was  developed  in  the  cutting  of  ornamental 
forms. 

The  Romans  used  lime  mortar  in  their  ordinary  construction. 
They  also  discovered  that  if  certain  materials  of  volcanic  origin 
were  pulverized  and  mixed  with  lime,  the  resulting  mortar  possessed 
the  property  of  hardening  under  water.  The  mortar  used  by  the 
Romans  in  their  aqueducts  and  other  hydraulic  works  was  made 
from  this  material,  obtained  from  near  the  foot  of  Vesuvius. 
Similar  materials  were  later  found  and  used  in  Germany  and  France. 

ART.   3.    RECENT  DEVELOPMENTS 

5.  The  Cement  Industry. — The  discovery  by  the  Romans  of 
the  hydraulic  properties  of  volcanic  lava,  and  the  location  of  other 
materials  possessing  the  same  properties,  made  possible  the  con- 
struction of  subaqueous  masonry  work.  No  considerable  progress, 
however,  was  made  in  such  work. 

About  the  middle  of  the  eighteenth  century  Smeaton,  a  noted 
English  engineer,  discovered  that  lime  made  from  certain  limestones 
containing  clay  possessed  hydraulic  properties.  This  discovery 
opened  new  possibilities  in  under-water  work,  and  these  hydraulic 
limes  were  used  to  a  limited  extent  during  the  next  half  century. 

In  1796  James  Parker,  an  Englishman,  burned  limestone  con- 


6  DEVELOPMENT  OF  MASONRY  CONSTRUCTION 

taining  a  larger  proportion  of  clay  and  ground  the  product.  He 
thus  produced  the  first  natural  cement,  which  he  called  Roman 
cement.  This  process  was  patented,  and  the  manufacture  of  natural 
cement  resulted. 

In  1818  Canvas  White,  an  engineer  of  the  Erie  Canal,  located 
rock  suitable  for  making  natural  cement  in  Madison  County,  New 
York,  and  the  first  cement  produced  in  the  United  States  was  made 
in  the  same  year.  Five  years  later  the  manufacture  of  natural 
cement  was  begun  at  Rosendale,  New  York.  The  production  of 
cement  in  this  region  extended,  and  cement  was  thus  provided  for 
most  of  the  hydraulic  construction  in  this  country  for  a  considerable 
period.  Later,  as  the  development  of  the  country  proceeded,  and 
demands  for  cement  increased,  deposits  of  cement  rock  were  found 
at  many  other  places.  Natural  cement  plants  were  established 
along  the  James  River  in  Virginia;  in  the  Lehigh  Valley,  in  Pennsyl- 
vania; at  Louisville,  Kentucky;  Utica,  Illinois;  Milwaukee,  Wis- 
consin, and  a  number  of  other  localities. 

In  1824  Joseph  Aspdin,  of  Leeds,  England,  discovered  that  by 
burning  a  mixture  of  slaked  lime  and  clay  at  high  temperature, 
hydraulic  cement  was  produced.  Aspdin  named  this  material 
Portland  Cement,  on  account  of  its  resemblance  to  Portland  stone, 
then  largely  used  in  England.  In  1845  the  manufacture  of  Port- 
land cement  was  begun  on  a  commercial  scale  by  J.  B.  White  &  Sons, 
in  Kent. 

During  the  period  between  1830  and  1850  Vicat,  in  France, 
made  a  number  of  studies  which  were  of  great  value  in  extending 
knowledge  of  the  new  material.  Plants  were  soon  established  in 
France  and  Germany  for  the  manufacture  of  Portland  cement,  and 
the  industry  became  an  important  one  throughout  Europe.  During 
the  next  few  years,  1865  to  1880,  John  Grant  made  a  series  of  investi- 
gations of  the  properties  of  Portland  cement  and  methods  of  using 
it  in  mortars  and  concrete.  His  papers  before  the  Institution  of 
Civil  Engineers  had  a  marked  influence  in  shaping  the  methods  of 
use  of  cement. 

From  1880  to  1900  the  Portland  cement  industry  developed 
rapidly  in  Europe,  and  numerous  studies  were  made  concerning  the 
composition  and  properties  of  the  material.  LeChatelier,  Alex- 
andre,  Candlot,  and  Feret,  in  France,  Tetmajer  in  Switzerland, 
Michaelis  and  Bohme  in  Germany,  Faija  in  England,  and  a  number 
of  others,  investigated  all  phases  of  the  subject,  greatly  improving 
the  quality  of  the  cement  and  showing  methods  of  employing  it  in 
construction  to  secure  the  best  results. 


RECENT  DEVELOPMENTS  7 

In  1875  Mr.  D.  O.  Saylor  began  the  manufacture  of  cement  at 
Coplay,  Pennsylvania.  From  this  beginning,  the  American  Port- 
land cement  industry  has  developed.  Great  improvements  in 
methods  of  manufacture  and  in  the  control  of  the  character  of  the 
product  have  been  made  in  this  country.  The  studies  of  Newberry, 
Richardson,  and  others  have  contributed  to  definite  knowledge  of 
the  proper  composition  of  the  material,  while  committees  of  the 
National  Engineering  Societies  and  many  independent  investigators 
have  perfected  methods  of  testing  cement  and  of  using  it  in  con- 
struction. 

This  industry  has  now  reached  immense  proportions  in  the 
United  States,  and  the  use  of  Portland  cement  has  extended  in  all 
directions,  modifying  largely  the  types  and  methods  of  construction 
used  in  all  classes  of  structures. 

6.  Reinforced  Concrete. — In  the  early  use  of  concrete,  it 
was  commonly  employed  as  a  filler  in  heavy  construction,  and  was 
not  possessed  of  great  strength.  Walls  of  concrete  were  usually 
protected  by  facings  of  stone  or  brick  masonry.  In  recent  years, 
however,  the  availability  of  cementing  materials  of  high  grade  has 
made  possible  the  use  of  concrete  in  many  classes  of  construction 
for  which  stone  or  brick  masonry  was  formerly  employed.  The 
facility  with  which  concrete  may  be  applied  to  many  uses  makes 
it  highly  desirable  material,  and  since  the  introduction  of  Portland 
cement  its  use  has  rapidly  increased.  This  use  has  been  further 
extended  in  the  past  few  years  by  the  development  of  reinforced 
concrete  construction.  In  1850  Lambot,  in  France,  constructed 
a  boat  of  reinforced  concrete,  and  in  1855  patented  his  invention 
in  England.  Fra^ois  Coignet,  in  1861,  applied  reinforced  concrete 
to  the  construction  of  beams,  arches,  pipes,  etc. 

In  1861  Joseph  Monier,  a  gardener  of  Paris,  constructed  tubs 
and  small  water  tanks  of  concrete  in  which  a  wire  frame  was 
imbedded.  In  1867  Monier  patented  his  reinforcement,  which 
consisted  of  a  mesh  formed  of  wires  or  rods  placed  at  right  angles 
to  each  other.  He  also  exhibited  some  work  at  the  Paris  Exposi- 
tion in  the  same  year.  Nothing  came  of  this  invention  for  a  number 
of  years,  but  in  1887  Wayss  and  Bauschinger  published,  hi  Germany, 
the  results  of  an  investigation  showing  the  value  of  the  Monier 
system,  and  giving  formulas  for  use  in  design. 

The  next  few  years  saw  considerable  development  of  this  type 
of  construction  in  Austria,  and  Melan,  an  Austrian  engineer,  invented 
a  system  of  reinforcement  for  arches  in  which  I-beams  were  bent 
to  the  form  of  the  arch  and  enclosed  in  concrete.  Hennebique, 


8  DEVELOPMENT  OF  MASONRY  CONSTRUCTION 

in  France,  began  making  reinforced  concrete  slabs  about  1880,  and 
patented  his  system  of  slab  reinforcement  in  1892. 

The  first  use  of  reinforced  concrete  in  the  United  States  seems 
to  have  been  by  Ernest  L.  Ransome,  in  1874.  The  next  year  W.  E. 
Ward  constructed  a  building  in  New  York,  in  which  reinforced 
concrete  walls,  roof,  and  floor  beams  were  used.  In  1877  H.  P. 
Jackson  used  reinforced  concrete  in  building  construction  in  San 
Francisco.  About  1884  Ransome  began  applying  reinforced  con- 
crete to  important  work  in  California,  and  in  that  year  took  out 
a  patent  for  the  first  deformed  bar. 

In  1894  the  Melan  system  of  arch-bridge  construction  was  intro- 
duced into  the  United  States  by  Mr.  Fr.  von  Emperger,  who  built 
the  first  important  arch  bridges.  At  about  the  same  time  Mr. 
Edwin  Thacher  began  the  construction  of  arch  bridges  using  bar 
reinforcement. 

During  the  period  from  1890  to  1900  the  use  of  reinforced  con- 
crete steadily  increased,  while  the  applications  of  plain  concrete 
had  been  extending  rapidly,  as  the  increasing  supply  of  cement 
provided  material  for  a  better  grade  of  construction. 

Since  1900  the  use  of  reinforced  concrete  has  rapidly  increased. 
The  use  of  massive  slab  construction  for  railroad  bridges  was  intro- 
duced by  the  C.  B.  &  Q.  Railroad  at  Chicago.  Fireproof  building 
construction  of  concrete  has  become  common,  and  concrete  has 
become  the  standard  material  for  short-span  highway  bridges. 
Many  investigations  have  been  made  concerning  the  properties  of 
the  materials  and  the  strengths  of  various  structural  forms;  the 
work  of  Considere,  in  France,  and  of  Talbot  at  the  University  of 
Illinois,  being  specially  notable.  Principles  for  rational  design  have 
been  established  and  recognized  standards  of  practice  are  rapidly 
forming. 


CHAPTER  II 
CEMENTING  MATERIALS 

ART.   4.     LIME 

7.  Classification. — The  cementing  materials  employed  in  the 
construction  of  masonry  and  concrete  structures  include  common 
lime,  hydraulic  lime,  Portland  cement,  natural  cement,  and  puzzolan. 
These  materials  are  formed  by  the  calcination  of  limestones,  or  of 
mixtures  of  limestones  with  siliceous  or  argillaceous  materials,  and 
their  properties  vary  with  the  nature  and  porportions  of  the  sub- 
stances combined  in  them. 

Common  Lime. — When  limestone  composed  of  nearly  pure  car- 
bonate of  lime  is  burned,  the  resulting  clinker,  known  as  quicklime, 
possesses  the  property  of  breaking  up,  or  slaking,  upon  being  treated 
with  a  sufficient  quantity  of  water.  The  slaking  of  lime  is  due  to 
its  rapid  hydration  when  in  contact  with  water,  and  the  process 
is  accompanied  by  a  considerable  increase  in  the  volume  of  the  mass 
of  lime  and  by  a  rise  in  temperature.  If  the  quantity  of  water  be 
only  sufficient  to  cause  the  hydration  of  the  lime,  the  quicklime  is 
reduced  to  a  dry  powder;  while  if  the  water  be  in  excess  it  becomes 
a  paste. 

The  slaked  lime  thus  formed  possesses  the  further  property, 
when  mixed  to  a  paste  with  water  and  allowed  to  stand  in  the  air, 
of  hardening  and  adhering  to  any  surface  with  which  it  may  be 
in  contact.  This  hardening  of  common  limes  will  take  place  only 
when  exposed  to  the  air  and  allowed  to  become  dry. 

When  lime  is  nearly  pure  and  its  activity  very  great  it  is  known 
Sisfat  lime. 

If  the  lime  have  mixed  or  in  combination  with  it  considerable 
impurities  of  inert  character,  which  act  as  an  adulteration  to  lessen 
the  activity  of  the  lime,  causing  a  partial  loss  of  the  property  of 
slaking  and  diminishing  its  power  to  harden,  it  is  known  as  meager 
or  poor  lime. 

Hydraulic  Lime. — When  the  limestone  contains  about  10  to 
20  per  cent  of  silica  or  clay  mixed  with  the  carbonate  of  lime,  the 

9 


10  CEMENTING  MATERIALS 

material  resulting  from  the  burning  is  known  as  hydraulic  lime. 
This  clinker  will  slake  when  treated  with  water  like  common  lime, 
but  with  reduced  activity.  The  slaked  lime  thus  obtained  pos- 
sesses the  further  property,  when  mixed  with  water  to  a  paste, 
of  hardening  under  water  and  without  contact  with  the  air. 

In  hydraulic  lime  the  silica  and  alumina  are  combined  with  a 
portion  of  the  lime,  forming  compounds  which  harden  under  water, 
while  part  of  the  lime  is  left  uncombined.  This  free  lime  expands 
when  hydrated  by  addition  of  water,  causing  the  material  to 
slake. 

Hydraulic  Cement. — When  the  proportion  of  siliceous  or  argil- 
laceous materials  in  limestone,  or  mixed  with  it,  is  sufficient  to 
combine  with  all  the  lime,  leaving  no  lime  in  a  free  state,  the  prod- 
uct of  burning  is  known  as  hydraulic  cement.  This  clinker  will 
not  slake,  but  must  be  reduced  to  powder  by  grinding.  The  cement 
powder,  when  mixed  with  water,  has  the  property  of  setting  and 
hardening  under  water,  and  of  adhering  firmly  to  any  surface  with 
which  it  may  be  in  contact. 

Portland  Cement  is  the  name  given  to  hydraulic  cement  which 
is  formed  by  burning  and  grinding  an  intimate  mixture  of  powdered 
limestone  and  argillaceous  matter  in  accurately  determined  pro- 
portions. In  making  Portland  cement,  the  ingredients  are  care- 
fully proportioned  to  secure  the  complete  combination  of  the  lime 
with  the  silica  and  alumina  into  active  material,  and  it  is  necessary 
to  reduce  the  materials  to  a  very  fine  state  and  secure  uniform 
incorporation  of  the  ingredients  before  burning. 

Natural  Cements  are  made  by  burning  limestones  which  con- 
tain proper  proportions  of  argillaceous  materials,  and  grinding  the 
resulting  clinker  to  powder.  Natural  cements  are  less  rich  in  lime 
than  Portland  cements,  complete  combination  of  the  argillaceous 
materials  not  being  effected.  They  are  burned,  like  lime,  without 
the  pulverization  of  the  raw  materials,  and  require  a  much  lower 
temperature  in  burning  than  Portland  cement. 

The  term  Puzzolan  is  commonly  applied  to  a  class  of  materials 
which,  when  made  into  a  mortar  with  fat  lime  or  feebly  hydraulic 
lime,  impart  to  the  lime  hydraulic  properties  and  cause  the  mortar 
to  harden  under  water.  It  derives  its  name  from  Pozzuoli,  a  city 
of  Italy  near  the  foot  of  Mount  Vesuvius,  where  its  properties  were 
first  discovered.  It  was  extensively  used  by  the  Romans  in  their 
hydraulic  constructions,  being  mixed  with  slaked  lime  for  the  for- 
mation of  hydraulic  mortar.  Puzzolan  is  essentially  a  silicate  of 
alumina  in  which  the  silica  exists  in  a  condition  to  be  attacked 


LIME  11 

readily  by  caustic  alkalies,  and  hence  easily  combines  with  the  lime 
in  the  mortar. 

Puzzolan  Cement  is  formed  by  mixing  slaked  lime  with  puzzolan 
and  grinding  the  mixture  to  a  fine  powder.  Certain  materials  of 
volcanic  origin  are  frequently  used  for  this  purpose  in  Europe, 
while  considerable  quantities  of  cement  of  this  class  have  been  made 
by  the  use  of .  blast  furnace  slag,  both  in  Europe  and  the  United 
States. 

8.  Common  Lime. — Common  lime  is  such  as  does  not  possess 
hydraulic  properties.  It  is  divided  into  fat  or  rich  lime  and  meager 
lime,  according  to  the  quantity  of  impurities  of  an  inert  character 
it  may  contain.  When  made  into  paste  and  left  in  air  it  slowly 
hardens.  The  process  of  hardening  consists  in  the  gradual  forma- 
tion of  carbonate  of  lime  through  the  absorption  of  carbonic  acid 
from  the  air,  accompanied  by  the  crystallization  of  the  mass  of 
hydrated  lime  as  it  gradually  dries  out.  In  common  lime  the  final 
hardening  takes  place  very  slowly,  working  inward  from  the  surface, 
as  it  is  dependent  upon  contact  of  the  mortar  with  the  air.  When 
the  lime  is  nearly  pure  the  resulting  carbonate  is  likely  to  be  some- 
what soluble,  and  consequently  to  be  injured  by  exposure.  Nearly 
all  limes,  however,  contain  small  amounts  of  silica  and  alumina, 
and  these  ingredients,  even  when  in  quantities  too  small  to  render 
the  lime  hydraulic,  impart  a  certain  power  to  set,  causing  the  harden- 
ing to  take  place  with  greater  rapidity  and  without  entire  dependence 
upon  contact  with  air.  It  also  renders  the  material  less  soluble 
and  more  durable  in  exposed  situations. 

Nearly  pure  limes,  consisting  mainly  of  calcium  oxide,  are  very 
caustic  and  become  hydrated  very  rapidly  when  brought  into  con- 
tact with  water.  This  hydration,  or  slaking,  produces  a  rise  in 
temperature  and  increase  in  volume,  which  vary  in  amount  accord- 
ing to  the  purity  of  the  lime,  the  volume  being  doubled  or  tripled 
for  good  fat  lime.  When  the  lime  is  derived  from  a  magnesian 
limestone,  it  may  contain  a  considerable  proportion  of  magnesia 
mixed  with  the  lime.  Limes  containing  more  than  about  15  per 
cent  of  magnesia  are  usually  called  magnesian  limes.  The  presence 
of  magnesia  has  the  effect  of  rendering  the  lime  less  active,  causing 
it  to  expand  less  upon  slaking.  The  magnesian  limes  harden  more 
slowly,  but  usually  gain  a  higher  ultimate  strength  than  the  high- 
calcium  limes. 

The  common  method  of  slaking  lime  consists  in  covering  the 
quicklime  with  water,  using  two  or  three  times  the  volume  of  the 
lime.  This  method  is  known  as  drowning.  The  lime  is  usually 


12  CEMENTING  MATERIALS 

spread  out  in  a  layer  perhaps  6  or  8  inches  thick,  in  a  mixing  box, 
the  water  poured  over  it  and  allowed  to  stand.  Sufficient  time 
must  be  allowed  for  all  of  the  lumps  to  be  reduced.  When  the 
lime  contains  much  foreign  matter,  the  operation  frequently  requires 
several  days.  Too  great  quantity  of  water  is  to  be  avoided,  the 
amount  being  such  as  will  reduce  the  lime  after  slaking  to  a  thick 
pasty  condition.  All  the  water  should  be  added  at  once,  as  the 
addition  of  water  after  the  hydration  is  in  progress  causes  a  lower- 
ing of  temperature  and  checks  the  slaking.  For  the  same  reason, 
the  lime  should  be  covered  after  adding  water,  and  not  stirred  or 
disturbed  until  the  slaking  is  completed.  The  covering  is  often 
effected  by  spreading  a  layer  of  sand  over  the  lime,  the  sand  being 
afterward  used  to  mix  with  it  in  making  mortar. 

A  second  method  of  slaking  is  sometimes  employed  having  for 
its  object  the  reduction  of  the  slaked  lime  to  powder,  and  known  as 
slaking  by  immersion.  This  is  accomplished  in  two  ways.  By  the 
first  method,  the  lime  is  suspended  in  water  in  baskets  for  a  brief 
period  to  permit  the  absorption  of  the  necessary  water,  after  which 
it  is  removed  and  covered  until  slaking  takes  place  and  the  lime 
falls  to  powder.  By  the  second  method,  sprinkling  is  substituted 
for  immersion,  the  lime  being  placed  in  heaps  and  sprinkled  with 
the  necessary  quantity  of  water,  then  covered  with  sand  and  allowed 
to  stand. 

Lime  is  commonly  sold  as  quicklime,  and  should  be  in  lumps  and 
not  air  slaked.  When  it  is  old  and  has  been  exposed  to  the  air  it 
is  likely  to  have  absorbed  both  moisture  and  carbonic  acid,  thus 
becoming  less  active,  the  portion  combined  with  carbonic  acid  being 
inert.  A  simple  test  of  the  quality  of  quicklime  is  to  immerse  a 
lump  for  a  minute,  then  place  in  a  dish  and  observe  whether  it  swells, 
cracks,  and  disintegrates,  with  a  rise  of  temperature. 

Slaking  some  days  in  advance  of  use  is  desirable  in  order  to 
insure  the  complete  reduction  of  the  lime,  and  it  is  quite  common 
to  slake  lime  several  weeks  before  it  is  to  be  used. 

Common  lime  is  ordinarily  used  in  construction  as  a  mortar, 
mixed  with  sand.  The  quantity  of  lime  in  the  mortar  should  be 
just  sufficient  to  fill  the  voids  in  the  sand,  without  leaving  any  part 
formed  entirely  of  lime.  Mortar  of  rich  lime  shrinks  in  hardening, 
while  masses  composed  entirely  of  lime  on  the  interior  are  likely 
to  remain  soft,  so  that  an  excess  of  lime  may  be  an  element  of  weak- 
ness. If  too  little  lime  be  used  the  mortar  may  be  porous  and  weak. 
The  proportions  ordinarily  required  are  between  one  part  lime  to 
two  parts  sand,  and  one  part  lime  to  three  parts  sand. 


LIME  13 

In  mixing  lime  mortar,  sand  is  spread  over  the  lime  paste  and 
worked  into  it  with  a  shovel  or  hoe.  The  proper  proportions  of 
sand  and  lime  may  be  judged  by  observing  how  the  mortar  works. 
If  too  much  sand  be  used  it  will  be  brittle,  or  "  short  ";  while  too 
much  paste  will  cause  it  to  stick  and  cake  so  that  it  will  not  flow 
from  the  trowel. 

Mortar  of  common  lime  should  not  be  employed  in  heavy  masonry 
or  in  damp  situations.  Where  the  mass  of  masonry  is  large,  the 
lime  mortar  will  become  hardened  with  great  difficulty,  and  after 
a  long  time.  The  penetration  of  the  final  induration  due  to  the 
absorption  of  carbonic  acid  is  very  slow.  The  observations  of 
M.  Vicat  showed  that  carbonization  extended  only  a  few  millimeters 
the  first  year  and  afterward  more  slowly.  The  induration  of  the 
lime  along  the  surfaces  of  contact  with  a  harder  material  is  usually 
more  rapid  than  in  the  interior  of  the  mass  of  lime,  and  the  strength 
of  adhesion  to  stone  or  brick  is  often  greater  than  that  of  cohesion 
between  the  particles  of  mortar. 

9.  Hydraulic  Lime. — Hydraulic  lime  is  obtained  by  burning 
limestone  containing  silica  and  alumina  in  sufficient  quantities 
to  impart  the  ability  to  harden  under  water.  The  hydraulic  elements 
are  present  in  such  quantities  that  they  combine  with  a  portion 
of  the  lime,  forming  silicates  and  aluminates  of  lime,  leaving  the 
remainder  as  free  lime  in  an  uncombined  state. 

The  hydraulic  activity  of  a  lime  or  cement,  that  is,  its  ability 
to  harden  under  water,  depends  primarily  upon  the  relative  propor- 
tions of  the  hydraulic  ingredients  and  of  lime.  Silica  and  alumina 
are  considered  to  be  the  effective  hydraulic  ingredients,  and  it  is 
common  to  designate  the  ratio  of  the  sum  of  the  weights  of  silica 
and  alumina  to  that  of  lime  in  the  material  its  hydraulic  index. 
The  hydraulic  index  gives,  therefore,  within  certain  limits,  a  measure 
of  the  hydraulicity  of  the  various  classes  of  limes.  It  is  to  be  remem- 
bered, however,  that  there  are  other  factors  to  be  considered  in 
judging  of  the  action  of  lime  than  this  simple  proportion.  The  other 
ingredients  may  by  their  combinations  withdraw  portions  of  the 
active  elements  so  as  to  modify  the  effective  ratio  between  them, 
while  the  activity  of  the  lime  depends  largely  upon  the  state  of 
combination  in  which  the  active  elements  exist.  This  is  not  shown 
by  analysis,  and  may  be  greatly  modified  by  the  manipulation 
given  the  material  during  manufacture. 

Limes  with  hydraulic  index  less  than  10/100  possess  little  if 
any  hydraulic  properties,  and  are  known  as  common  limes.  When 
the  hydraulic  index  is  between  10/100  and  20/100  the  lime  is  feebly 


14  CEMENTING  MATERIALS 

hydraulic,  and  may  require  from  twelve  to  twenty  days  to  set  under 
water.  Hydraulic  lime  proper  includes  that  of  index  from  about 
20/100  to  40/100.  These  may  harden  in  from  two  to  eight  or  ten 
days. 

The  quantity  of  free  lime  in  the  material  is  dependent  upon 
the  degree  of  burning,  as  well  as  upon  the  amount  of  lime  contained 
by  the  stone.  If  the  stone  be  underburned,  the  combination  of 
the  hydraulic  elements  with  the  lime  is  not  complete,  and  more 
of  the  lime  remains  in  a  free  state.  For  this  reason,  a  stone  of 
high  hydraulic  index  may,  when  underburned,  yield  a  lime,  but 
burned  at  a  high  temperature  becomes  unslakable.  The  best  limes 
are  usually  those  which  can  be  burned  at  a  high  temperature  to 
complete  the  chemical  combinations.  It  is  necessary  that  sufficient 
free  lime  be  present  to  cause  the  lime  to  slake  properly,  but  it  is 
also  desirable  that  the  quantity  of  uncombined  lime  be  as  small  as 
possible,  as  the  setting  properties  are  due  to  the  silicates  and  alu- 
minates,  while  the  hydrated  lime  remains  inert  during  the  initial 
hardening  of  the  mortar. 

According  to  Professor  LeChatelier,  limestone  for  hydraulic  lime 
should  contain  but  little  alumina,  as  the  aluminates  are  hydrated 
during  the  slaking  of  the  lime,  while  the  silicates  are  not  affected, 
the  heat  of  the  slaking  preventing  their  hydration. 

The  following  is  given  as  an  average  analysis  of  the  best  French 
hydraulic  lime: 

Silica 22 

Alumina 2 

Oxide  of  iron 1 

Lime ...  63 

Magnesia 1.5 

Sulphuric  acid 0.5 

Water.  .  10 


100 

It  is  important  that  the  slaking  be  very  thorough,  as  the  pres- 
ence of  unhydrated  free  lime  in  the  mortar  while  hardening  is  an 
element  of  danger  to  the  work.  Any  lime  becoming  hydrated  after 
the  setting  of  the  mortar  may,  by  its  swelling,  cause  distortion  and 
perhaps  disintegration  of  the  mortar. 

After  the  lime  has  been  reduced  to  powder  by  slaking,  it  is  forced 
through  sieves  which  permit  the  passage  of  all  pulverized  particles 
but  hold  those  of  appreciable  size,  including  the  underburned  rock 


LIME  15 

and  the  overburned  parts  which  refuse  to  slake.  The  residue  left 
from  the  sifting  of  hydraulic  lime  is  known  as  grappiers.  This 
material  is  mainly  composed  of  hard  material  more  rich  in  silica 
and  alumina  than  the  other  portions  of  the  lime.  The  grappiers 
are  frequently  ground  and  sold  as  cement,  and  when  properly  handled 
may  form  cement  of  fairly  good  quality. 

10.  Hydrated  Lime. — When  quicklime  is  slaked  with  the  quantity 
of  water  necessary  completely  to  hydrate  it,  and  the  resulting  mate- 
rial is  bolted  to  remove  all  unslaked  particles,  the  result  is  a  very 
fine  white  powder,   commercially  known  as  hydrated  lime.     This 
lime  is  sold  on  the  market  in  barrels  or  bags,  and  it  is  in  convenient 
form  for  use.     Lime  in  this  form  may  be  kept  for  considerable 
periods  without  deterioration,  provided  it  is  protected  from  con- 
tact with  moisture. 

Hydrated  lime  ordinarily  weighs  about  40  pounds  per  cubic 
foot,  and  contains  approximately  75  per  cent  of  quicklime.  By 
mixing  with  about  an  equal  weight  of  water,  it  may  be  reduced  to 
lime  paste,  or  lime  putty,  as  it  is  commonly  called  in  building  oper- 
ations. Lime  paste  occupies  a  slightly  greater  volume  than  the 
hydrated  lime  from  which  it  is  prepared. 

The  use  of  hydrated  lime  for  mixing  with  cement  mortar  in 
ordinary  masonry  construction  is  rapidly  increasing.  It  is  also 
frequently  used  in  small  proportions  in  Portland  cement  concrete 
to  make  the  concrete  flow  more  smoothly,  and  sometimes  to  decrease 
the  permeability  of  the  mortar.  (See  Art.  23.) 

11.  Specifications   for   Lime. — In   ordinary   building   operations 
lime  is  commonly  employed  in  the  form  of  quicklime  and  slaked 
where  used.     Usually  the  quality  of  the  lime  has  been  judged  by 
its  activity  in  slaking  and  no  particular  tests  are  specified.     Tests 
of  composition  by  chemical  analysis  and  of  completeness  of  slaking 
by  washing  through  sieves  are,  however,  frequently  employed. 

Hydrated  lime  is  now  largely  used  for  mixing  with  cement  mortar 
and  for  plastering  work,  and  this  use  is  rapidly  extending.  The 
tests  employed  for  hydrated  lime  include  chemical  analysis,  fine- 
ness, and  permanence  of  volume  or  soundness. 

The  American  Society  for  Testing  Materials  has  adopted  standard 
specifications  giving  methods  for  making  these  tests.  These  speci- 
fications are  given  in  the  Book  of  Standards  of  the  Society  or  may 
be  obtained  in  pamphlet  form  from  the  Secretary  of  the  Society. 
As  they  are  now  undergoing  revision  they  are  subject  to  change 
and  will  not  be  given  here. 


16  CEMENTING  MATERIALS 

ART.  6.    HYDRAULIC   CEMENT 

12.  Setting  and  Hardening  of  Cement. — When  cement  powder 
is  mixed  with  water  to  a  plastic  condition  and  allowed  to  stand, 
it  gradually  combines  into  a  solid  mass,  taking  the  water  into  con- 
bination,  and  soon  becomes  firm  and  hard.  This  process  of  com- 
bination among  the  particles  of  the  cement  is  known  as  the  setting 
of  the  cement. 

Cements  of  different  character  differ  very  widely  in  their  rate 
and  manner  of  setting,  some  occupying  but  a  few  minutes  in  the 
operation,  while  others  require  several  hours.  Some  begin  setting 
immediately  and  take  considerable  time  to  complete  the  set,  while 
others  stand  for  considerable  time  with  no  apparent  action  and 
then  set  very  quickly. 

The  points  where  the  set  is  said  to  begin  and  end  are  necessarily 
arbitrarily  fixed,  and  are  determined  by  finding  when  the  mortar 
will  sustain  a  needle  carrying  a  specified  weight.  The  initial  set 
is  supposed  to  be  when  the  stiffening  of  the  mass  has  become  per- 
ceptible; the  final  set,  when  the  cohesion  extends  through  the  mass 
sufficiently  to  offer  such  resistance  to  any  change  of  form  as  to 
cause  rupture  before  deformation  can  take  place. 

After  the  completion  of  the  setting  of  the  cement,  the  mortar 
continues  to  increase  in  cohesive  strength  over  a  considerable  period 
of  time,  and  this  subsequent  development  of  strength  is  called  the 
hardening  of  the  cement. 

The  process  of  hardening  appears  to  be  quite  distinct  from, 
and  independent  of,  that  of  setting.  A  slow-setting  cement  is  apt, 
after  the  first  day  or  two,  to  gain  strength  more  rapidly  than  a 
quick-setting  one;  but  it  does  not  necessarily  do  so.  The  ultimate 
strength  of  the  cement  is  also  quite  independent  of  the  rate  of  setting. 
A  cement  imperfectly  burned  may  set  more  quickly  and  gain  less 
ultimate  strength  than  the  same  cement  properly  burned,  but  of 
two  cements  of  different  composition  the  quicker-setting  may  be 
the  stronger. 

There  is  as  wide  variation  in  the  rate  of  hardening  of  different 
cements  as  in  the  rate  of  setting;  some  gain  strength  rapidly  and 
attain  their  ultimate  strengths  in  a  few  weeks,  while  others  harden 
much  more  slowly  at  first  and  continue  to  gain  in  strength  for  several 
years.  The  rate  of  early  hardening  gives  but  little  indication  of 
the  ultimate  action  of  the  cement,  as  the  final  strength  of  the  mortar 
may  be  the  same  however  rapidly  the  strength  is  attained. 

The  rate  at  which  cement  sets  seems  to  depend  upon  the  pres- 


HYDRAULIC  CEMENT  17 

ence  of  certain  aluminates  of  lime,  the  rapidity  of  set  increasing 
with  the  percentage  of  alumina  in  the  material.  The  final  harden- 
ing is  attributed  mainly  to  the  silicates  of  lime,  which  are  the  impor- 
tant elements  in  giving  strength  and  durability  to  the  mortar.  The 
formation  of  these  active  elements  in  the  cement  depends  upon 
the  manipulation  of  the  material  in  manufacture,  as  well  as  upon 
the  composition  of  the  raw  materials.  In  an  underburned  cement, 
the  relative  proportions  of  aluminates  to  silicates  is  large  and  the 
set  is  rapid. 

Calcium  Sulphate. — The  addition  of  a  small  amount  of  sulphate 
of  lime  to  cement  has  the  effect  of  slackening  the  rate  of  set.  Such 
addition  is  frequently  made  by  manufacturers  to  reduce  the  activity 
of  fresh  cement,  by  grinding  a  small  amount  of  gypsum  with  the 
cement. 

Effect  of  Sand. — Cement  is  ordinarily  employed  in  mortar  formed 
by  mixing  it  with  sand,  and  the  action  of  the  mortar  is  necessarily 
largely  affected  by  the  nature  and  quantity  of  sand  used. 

When  the  cement  is  finely  ground  and  the  sand  of  good  quality, 
a  mortar  composed  of  equal  parts  of  each,  as  a  general  thing,  finally 
attains  a  strength  as  high  as,  or  higher  than,  that  of  neat  cement. 
Cements  of  different  characters,  however,  vary  considerably  in  their 
power  to  "  take  sand  "  without  loss  of  strength;  some  of  the  weaker 
ones  may  not  be  able  to  take  more  than  half  their  weight  of  standard 
sand,  while  others  can  be  mixed  with  considerably  more  than  their 
own  weight  without  loss  of  strength  at  end  of  six  months  or  one 
year  after  mixing.  All  have  a  certain  limit  within  which  they  may 
be  made  stronger  by  an  admixture  of  good  sand  than  they  would 
be  if  mixed  neat. 

Clean  and  sharp  sand  usually  gives  higher  strength  in  mortar 
than  that  containing  admixtures  of  clay  or  earth,  or  that  composed 
of  rounded  grains,  coarse  sand  usually  giving  greater  strength  than 
that  which  is  very  fine.  It  is  often  difficult,  however,  to  judge  of 
the  quality  of  sand  without  experimenting  with  it.  In  some  cases 
a  small  amount  of  fine  clay  appears  to  increase  the  strength  of  mor- 
tar, while  a  judicious  mixture  in  the  sand  of  grains  of  various  sizes 
may  be  of  value  in  reducing  the  volume  of  interstices.  Mortar 
composed  of  sand  and  cement  usually  possesses  greater  ability  to 
adhere  to  other  surfaces  when  coarse  sand  is  used  that  when  the 
sand  is  fine. 

Effect  of  Water. — The  quantity  of  water  used  in  mixing  mortar 
is  one  of  the  most  important  elements;  the  less  the  quantity,  pro- 
vided there  be  sufficient  to  thoroughly  dampen  the  mass  of  cement, 


18  CEMENTING  MATERIALS 

the  quicker  the  set.  With  some  Portland  sements,  changing  the 
quantity  of  water  used  in  mixing  from  20  to  25  per  cent  of  the  weight 
doubles  or  even  triples  the  time  required  for  the  mortar  to  set. 

When  the  quantity  of  water  used  in  mixing  is  sufficient  to  reduce 
the  mortar  to  a  soft  condition,  the  hardening  as  well  as  the  setting 
becomes  slow,  and  the  strength  during  the  early  period  is  less  than 
when  a  less  quantity  of  water  is  used.  This  difference  disappears 
to  a  considerable  extent  with  time,  and  the  mortar  mixed  wet  may 
eventually  gain  as  much  strength  as  though  mixed  with  less  water. 

Cement  mortar  kept  under  water  hardens  more  rapidly  in  the 
early  period  than  that  exposed  to  the  ah*.  Nearly  any  cement 
mortar  will  harden  more  rapidly  and  gain  greater  strength  if  kept 
moist  during  the  operation  of  setting  and  the  first  period  of  harden- 
ing than  if  it  be  exposed  at  that  time  to  dry  air.  Sudden  drying 
out  about  the  time  of  completing  setting  causes  a  considerable  loss 
of  strength  in  cement  mortar,  and  frequently  the  mortar  so  treated 
is  filled  with  drying  cracks.  This  result  is  usually  more  marked 
when  the  mortar  has  been  mixed  quite  wet. 

Effect  of  Temperature. — The  temperature  of  the  water  used  in 
mixing  and  that  of  the  air  in  which  the  mortar  is  placed  during 
setting  has  an  important  bearing  upon  the  time  required  for  setting; 
the  higher  the  temperature,  within  certain  limits,  the  more  rapid 
the  set.  Some  cements  which  require  several  hours  to  set  when 
mixed  with  water  at  temperature  of  40°  F.  will  set  in  a  few  minutes 
if  the  temperature  of  the  water  be  increased  to  80°  F.  Below  a 
certain  inferior  limit,  ordinarily  from  30°  to  40°  F.,  the  mortar  sets, 
with  extreme  slowness  or  not  at  all,  while  at  a  certain  upper  limit, 
in  some  cements  between  100°  and  140°  F.,  a  change  suddenly 
occurs  from  very  rapid  to  very  slow  rate  of  set,  which  then  decreases 
as  the  temperature  increases  until  the  cement  ceases  to  set. 

The  temperature  of  the  air  or  water  in  which  the  mortar  is 
immersed  while  hardening  has  a  very  important  effect  upon  the  gain 
in  strength.  Heat  accelerates  the  action,  while  at  temperatures 
near  the  freezing-point  of  water  the  gain  in  strength  is  very  slow. 

13.  Portland  Cement. — The  term  Portland  cement  is  used  to 
Designate  material  formed  by  burning  to  incipient  fusion  a  finely 
ground  mixture  of  definite  proportions  of  limestone  and  argillaceous 
materials,  and  grinding  the  clinker  so  formed  to  fine  powder.  Several 
classes  of  materials  are  used  for  this  purpose.  Hard  limestone  or 
chalk,  consisting  of  nearly  pure  carbonate  of  lime,  is  frequently 
employed,  mixed  with  clay  or  shale  to  furnish  the  hydraulic  ingredi- 
ents. In  the  Lehigh  District  in  Pennsylvania  cement  rock,  con- 


HYDRAULIC  CEMENT  19 

sisting  of  limestone  containing  silica  and  alumina  in  sufficient  quanti- 
ties to  make  natural  cement  when  burned  alone,  is  mixed  with  nearly 
pure  limestone  to  obtain  the  proper  Portland  cement  composition. 
In  the  Michigan  district  marl  and  clay  excavated  in  soft  and  wet 
condition  are  used.  In  a  few  instances  limestone  is  mixed  with 
blast-furnace  slag  for  the  production  of  Portland  cement.  This 
is  quite  distinct  from  the  manufacture  of  slag  cement  (so  called) 
in  which  the  materials  are  not  burned  together. 

To  make  good  Portland  cement  it  is  always  necessary  that  the 
ingredients  be  very  carefully  proportioned  and  that  the  mixture 
be  very  homogeneous.  This  requires  the  pulverization  of  the  mate- 
rials and  their  uniform  incorporation  into  the  mixture  before  burning. 
The  burning  of  Portland  cement  requires  high  heat  to  insure 
complete  combination  of  the  lime  with  the  silica  and  alumina.  In 
underburned  cement,  a  part  of  the  lime  may  be  left  as  caustic  lime, 
uncombined  with  the  clay.  This  is  apt  to  produce  unsound  cement, 
which  may  swell  and  crack  after  being  used. 

The  action  of  Portland  cement  seems  to  depend  upon  the  for- 
mation, during  burning,  of  certain  silicates  and  aluminates  of  lime 
which  constitute  the  active  elements  of  the  cement,  the  other  ingre- 
dients being  considered  impurities.  The  ideal  cement  would  be 
that  in  which  the  proportion  of  lime  is  just  sufficient  to  combine 
with  all  the  silica  and  alumina  in  the  formation  of  active  material. 
If  there  be  a  surplus  of  clay  beyond  this  point,  it  forms  inert  material. 
Any  surplus  of  lime  remains  in  the  cement  as  free  lime  and  consti- 
tutes one  of  the  chief  dangers  in  the  use  of  cement,  as,  although 
it  may  not  prevent  the  proper  action  of  the  cement  when  used,  it 
may  cause  the  mortar  to  swell  afterward  and  become  cracked  and 
distorted  as  the  lime  slakes. 

As  perfect  homogeneity  is  not  attainable  in  practice,  it  is  always 
necessary  that  the  clay  be  somewhat  in  excess  in  order  that  free 
lime  be  not  formed.  The  amount  of  excess  of  clay  necessary  depends 
upon  the  thoroughness  of  the  burning  and  the  evenness  which  may 
be  reached  in  the  mixture  of  the  raw  materials. 

The  normal  composition  of  Portland  cement  is  usually  within 
the  following  limits: 

Silica 20       to  25  per  cent 

Alumina 5        to    9  per  cent 

Iron  oxide 2        to    5  per  cent 

Lime 59        to  65  per  cent 

Magnesia 0.5    to    3  per  cent 

Sulphuric  acid .  .  . 0.25  to    2  per  cent 


20  CEMENTING  MATERIALS 

After  the  cement  clinker  resulting  from  the  burning  is  sufficiently 
cooled,  it  is  put  through  grinders  and  reduced  to  a  fine  powder. 
The  degree  of  fineness  to  which  the  cement  is  ground  is  always 
very  important  in  its  effect  upon  the  strength  of  mortar  made  from 
the  cement.  The  valuable  part  of  the  cement  is  that  which  is  ground 
extremely  fine — to  an  impalpable  powder.  The  coarse  parts  are 
not  altogether  inert,  but  are  more  or  less  active,  depending  upon 
the  size  of  the  grains  of  which  they  are  composed. 

Cement  when  used  is  commonly  mixed  with  sand  and  the  attain- 
ment of  strength  in  sand  mortar,  rather  than  paste  of  neat  cement, 
is  of  importance.  The  more  finely  ground  the  cement,  the  greater 
its  resistance  when  mixed  with  sand,  both  in  the  earlier  and  later 
stages  of  hardening,  and  also  the  sooner  will  it  reach  its  ultimate 
strength.  The  effect  of  fine  grinding  is  much  greater  when  the 
proportion  of  sand  to  cement  is  large,  as  the  power  of  the  cement 
to  "  take  sand  "  without  diminution  of  strength  is  thereby  greatly 
increased.  The  coarser  particles  of  the  cement  may  be  considered 
as  practically  inert  material,  which  acts  as  sand  rather  than  as  cement 
in  the  mortar.  The  ability  of  the  cement  to  harden  and  develop 
"strength  in  sand  mortar  is  thus  dependent  upon  the  amount  of  fine 
material  contained  in  it. 

Portland  cement  made  from  materials  containing  very  small 
percentages  of  iron  oxide  are  very  light  in  color  or  white.  These 
cements  usually  contain  high  percentages  of  alumina,  and  are  con- 
sequently quick  setting.  They  are  lower  in  strength  than  normal 
Portlands. 

14.  Natural  Cement. — The  term  natural  cement  is  used  to  desig- 
nate a  large  number  of  widely  varying  products  formed  by  burning 
rock  without  pulverization  or  the  admixture  of  other  materials. 
These  cements  contain  larger  proportions  of  argillaceous  materials, 
with  less  lime,  than  Portland  cement,  and  are  burned  at  a  lower 
temperature. 

The  term  Roman  Cement  is  used  in  Europe  to  designate  a  class 
of  quick-setting  cements  formed  by  burning,  at  a  comparatively 
low  temperature,  limestone  containing  a  high  percentage  of  clay. 
The  proportion  of  alumina  in  these  materials  is  large  and  possibly 
accounts  for  the  quick  set.  Materials  of  this  character  become 
inert  when  the  temperature  of  burning  is  increased  to  the  point 
where  the  chemical  reactions  would  become  complete. 

A  class  of  materials  intermediate  between  the  Roman  cements 
and  the  Portland  cements  is  called  in  Europe  Natural  Portland 
Cement.  In  composition  they  are  similar  to  Portland  cement,  but 


HYDRAULIC  CEMENT  21 

contain  less  lime.  They  are  burned  at  a  higher  temperature  than 
Roman  cements,  and  are  usually  slower  setting.  Natural  cements 
made  in  the  Lehigh  region  are  of  this  character.  These  materials 
may  be  made  into  Portland  cement  by  addition  of  a  limestone  con- 
sisting of  more  nearly  pure  carbonate  of  lime. 

Magnesian  Natural  Cements  are  formed  by  burning  Magnesian 
limestones.  The  composition  of  these  cements  varies  from  that 
of  the  Roman  cements  to  that  in  which  the  proportion  of  magnesia 
is  as  great  as  that  of  lime.  The  action  of  cements  of  this  class  is 
somewhat  similar  to  that  of  the  Roman  cements.  They  may  be 
either  slow  or  quick  setting,  and  gain  strength  rather  slowly,  reach- 
ing a  much  less  ultimate  strength  than  Portland  cement.  Mag- 
nesian cements  are  but  little  used  in  Europe,  but  in  the  United 
States  they  constitute  the  larger  part  of  the  natural  cements  in  use, 
and  many  of  them  have  been  found  by  experience  to  be  very  useful 
and  reliable  materials. 

The  rock  from  which  natural  cements  are  made  differs  greatly 
in  character  in  the  same  locality,  and  in  different  strata  in  the  same 
quarry.  In  some  of  the  mills  the  nature  of  the  product  is  regulated 
by  mixing,  in  proper  proportions,  the  clinker  obtained  by  burning 
rock  from  different  strata.  Each  portion  of  the  rock  must  be  burned 
in  such  degree  as  is  suited  to  its  composition,  and  hence,  as  the 
material  is  not  pulverized  before  burning,  it  must  be  burned  sepa- 
rately and  mixed  afterward.  To  produce  uniformly  good  cement, 
therefore,  requires  close  and  careful  attention;  for  this  reason  there 
is  often  considerable  difference  in  the  quality  of  cement  made  by 
works  in  the  same  locality  and  from  very  similar  materials. 

Mixed  Cements. — In  localities  where  both  Portland  and  natural 
cements  are  made  by  the  same  works,  mixtures  of  the  lower  grades 
of  Portland  with  natural  cements  are  sometimes  made.  These  are 
usually  sold  as  natural  cements  under  the  name  Improved  Cements. 
The  effect  of  the  mixture  is  to  make  the  setting  slower,  and  to 
somewhat  increase  the  strength  of  the  natural  cement. 

15.  Puzzolan  Cement. — Puzzolan  cement  is  formed  by  mixing  and 
grinding  together  definite  proportions  of  slaked  lime  and  puzzolan. 
In  Germany  puzzolan  cement  is  made  by  the  use  of  a  natural  puz- 
zolan called  trass,  consisting  of  a  volcanic  earth.  In  the  United 
States  cement  of  this  character  is  made  by  the  use  of  specially  pre- 
pared blast-furnace  slag.  This  cement  is  sometimes  called  slag 
cement.  Basic  slag,  containing  lime  in  excess  of  the  silica  and  with 
a  high  alumina  content,  is  used  for  this  purpose.  It  is  made  granular 
by  quenching  in  cooling. 


22  CEMENTING   MATERIALS 

It  is  very  important,  in  making  slag  cements,  that  the  slag  be 
ground  very  fine,  and  be  very  intimately  mixed  with  the  lime.  The 
lime  is  slaked  and  bolted  and  then  ground  mechanically  with  the 
slag  so  as  to  insure  thorough  incorporation  into  the  mixture.  In 
some  of  the  European  plants  the  slag  is  finely  ground  and  bolted 
through  fine  sieves  before  being  mixed  with  the  lime,  but  more  com- 
mon practice  is  to  slake  and  bolt  the  lime  and  mix  with  the  granular 
slag  before  grinding,  or  to  do  the  pulverizing  of  the  slag  in  two 
stages  and  make  the  mixture  between  the  first  and  second 
grinding. 

Puzzolan  cement  is  usually  very  finely  ground,  and  is  slow  in 
setting.  It  is  sometimes  treated  with  soda  to  quicken  the  set. 
When  allowed  to  harden  in  dry  air,  it  is  likely  to  shrink  and  crack. 
When  used  for  under-water  work,  mortar  of  puzzolan  cement  fre- 
quently gives  nearly  the  same  strength  as  good  Portland  cement. 
It  is  essentially  a  hydraulic  material,  and  it  is  specially  important 
that  it  be  kept  damp  during  the  early  period  of  hardening,  in  order 
that  the  water  necessary  to  proper  hardening  may  not  evaporate. 

The  composition  of  slag  cement  usually  differs  from  that  of 
Portland  cement  in  having  a  less  quantity  of  lime,  more  silica  and 
alumina  and  more  alumina  in  proportion  to  silica. 

16.  Sand  Cement. — Sand  cement  is  the  name  given  to  material 
formed  by  grinding  together  Portland  cement  and  silica  sand  to 
extremely  fine  powder  and  a  very  intimate  mixture.  It  is  claimed 
that  a  considerable  amount  of  sand  may  be  thus  mixed  with  the 
cement  without  materially  reducing  the  strength  of  mortar  made 
by  mixing  the  resulting  cement  with  the  usual  proportions  of  sand. 
The  additional  grinding  reduces  all  of  the  cement  to  impalpable 
powder,  thus  increasing  the  amount  of  active  material. 

Sand  cement  as  ordinarily  made  contains  equal  proportions  of 
Portland  cement  and  silica  sand.  Cement  of  this  character  has 
recently  been  made  in  California  by  grinding  volcanic  rock,  or  tufa, 
with  Portland  cement.  The  tufa  used  is  a  puzzolan,  and  it  is  claimed 
that  it  reacts  with  the  lime  of  the  cement.  The  results  of  tests 
indicate  that  mortar  made  from  this  cement  is  equal  in  strength 
to  that  of  the  original  Portland.  Cement  of  this  kind  is  now  being 
made  by  the  U.  S.  Reclamation  Service  in  some  of  the  Western 
States  to  reduce  the  cost  of  concrete  work  where  Portland  cement 
is  expensive  and  difficult  to  get. 

Similar  methods  are  employed  in  Germany  where  a  puzzolan 
called  trass  is  used,  and  in  Italy  where  volcanic  lava  is  ground  with 
the  cement.  These  cements  are  used  for  work  in  sea  water  to  les- 


HYDRAULIC  CEMENT  23 

sen  the  action  of  the  sea  salts  upon  the  lime  salts  of  the  Portland 
cement. 

Sand  cement  has  frequently  been  used  for  the  purpose  of  secur- 
ing impermeable  mortar  where  waterproof  work  is  needed.  It  is 
useful  for  this  purpose  on  account  of  its  extreme  fineness. 

17.  Soundness  of  Cement. — The  permanence  of  any  structure 
erected  by  the  use  of  cement  is  dependent  upon  the  ability  of  the 
cement,  after  the  setting  and  hardening  processes  are  complete, 
to  retain  its  strength  and  form  unimpaired  for  an  indefinite  period. 
Experiment  has  shown  that  mortars  made  from  cement  of  good 
quality  frequently  continue  to  gain  strength  and  hardness  through 
a  period  of  several  years,  or  at  least  that  there  is  no  material  diminu- 
tion in  strength  with  time;  and  that  changes  of  temperature,  or 
in  the  degree  of  moisture  surrounding  it,  produce  no  injurious  effects 
upon  the  material.  This  durability  in  use  is  commonly  known  as 
the  permanence  of  volume  or  soundness  of  the  cement. 

When  mortar  which  has  been  immersed  in  water  is  transferred 
to  dry  air,  a  slight  contraction  may  take  place  in  volume,  together 
with  an  increase  in  strength;  while  a  transfer  the  other  way  may 
produce  the  opposite  result;  but"  no  distortion  of  form  or  disinte- 
gration of  the  mortar  will  take  place  in  either  case  if  the  cement 
be  of  good  quality. 

Sometimes  cement  when  made  into  mortar  sets  and  hardens 
properly,  and  later,  when  exposed  to  the  action  of  the  atmosphere 
or  water,  becomes  distorted  and  cracked  or  even  entirely  disinte- 
grated. If  the  composition  deviates  but  slightly  from  the  normal, 
this  process  of  disintegration  may  not  show  itself  for  a  considerable 
time  and  proceeds  very  slowly.  It  thus  becomes  an  element  of 
considerable  danger,  as  it  is  liable  to  escape  detection  in  testing 
the  cement. 

The  presence  of  small  quantities  of  free  lime  in  cement  is  doubt- 
less one  of  the  most  common  causes  of  disintegration  in  cement 
mortar.  The  lime  being  distributed  through  the  cement  in  small 
particles  is  hydrated  very  slowly  after  the  cement  has  set,  causing, 
through  its  swelling  during  slaking,  strong  expansive  forces  on  the 
interior  of  the  mortar,  and  producing  an  increase  of  volume,  loss 
of  strength,  and  perhaps  final  disintegration. 

Free  magnesia  in  cement  is  supposed  to  act  very  much  like  free 
lime.  The  action  of  magnesia,  however,  is  much  slower  than  that 
of  lime,  and  for  this  reason  is  a  more  serious  defect.  Specifications 
for  Portland  cement  frequently  limit  the  amount  of  magnesia  that 
may  be  present  in  the  cement. 


24  CEMENTING  MATERIALS 

Most  Portland  cements  probably  contain  small  amounts  of  the 
expansive  elements,  which  when  in  very  small  quantity  act  with 
extreme  slowness  and  perhaps  produce  no  visible  effect  for  several 
months  after  the  use  of  the  cement;  then  occurs  a  decrease  of 
strength,  which  disappears  with  time.  Cements  which  gain  strength 
rapidly  are  quite  apt  to  act  in  this  manner,  a  depression  in  the 
strength  curve  occurring  at  from  six  months  to  one  year  after  the 
mortar  is  made. 

Cements  for  use  in  sea  water  should  contain  very  little  alumina. 
Some  of  the  salts  in  the  sea  water  attack  these  alumina  compounds, 
causing  disintegration  of  the  cement  and  giving  rise  to  expansive 
action  which  cracks  and  breaks  up  the  work. 

The  presence  of  expansive  elements  in  Portland  cement  is  prob- 
ably due  to  incomplete  burning  or  lack  of  uniformity  in  the  incor- 
poration of  the  ingredients  rather  than  to  defective  composition. 

The  fineness  of  the  cement  modifies  the  action  of  the  free  lime, 
as  finely  divided  material  will  slake  more  quickly  than  coarse  grains, 
and  the  lime  is  more  apt  to  become  hydrated  before  setting;  or, 
if  the  cement  be  exposed  before  use,  the  lime  in  a  fine  state  will 
sooner  become  air  slaked. 

18.  Chemistry  of  Cement. — Professor  LeChatelier  was  the  first 
to  explain  the  composition  of  Portland  cement.  He  studied  sec- 
tions of  clinker  under  the  microscope,  and  examined  the  properties 
of  the  various  compounds  formed  by  the  principal  ingredients.  He 
concluded l  that  the  tricalcium  silicate,  3CaO,  SiO2,  is  the  only 
silicate  that  is  really  hydraulic,  and  that  it  is  the  essential  active 
element  in  cement.  In  Portland  cement  he  finds  it  to  be  the  princi- 
pal component,  occurring  in  cubical  crystals.  It  is  formed  by 
combination  of  silica  and  lime  in  presence  of  fusible  compounds 
formed  by  alumina  and  iron. 

"  The  dicalcium  silicate,  2CaO,  SiC>2,  possesses  the  singular 
property  of  spontaneously  pulverizing  in  the  furnace  upon  cooling. 
This  silicate  does  not  possess  hydraulic  properties  and  will  not 
harden  under  water. 

"  There  are  various  aluminates  of  lime,  all  of  which  set  rapidly 
in  contact  with  water.  The  most  important  is  the  tricalcium  alu- 
minate,  3CaO,  A12O3." 

Professor  LeChatelier  gives  two  limits  within  which  the  quantity 
of  lime  in  Portland  cement  should  always  be  found.  These  are, 
that  the  proportion  of  lime  should  always  be  greater  than  that 
represented  by  the  formula 

1  Annales  des  Mines,  September,  1893. 


HYDRAULIC  CEMENT  25 

CaO+MgO 

— i ~~~~ ^~  o% 

and  that  it  should  never  exceed  that  given  by  the  formula, 

CaO+MgO 

3. 


The  symbols  in  these  formulas  represent  the  number  of  equivalents 
of  the  substances  present,  not  the  weights. 

Messrs  S.  B.  and  W.  B.  Newberry  from  a  study  of  the  compounds 
of  silica  and  alumina  with  lime  reached  the  following  conclusions  :  1 

(1)  Lime  may  be  combined  with  silica  in  proportion  of  three  molecules  to 
one  and  still  give  a  product  of  practically  constant  volume  and  good  hardening 
properties,  though  hardening  very  slowly.     With  3|  molecules  of  lime  to  one 
of  silica  the  product  is  not  sound  and  cracks  in  water. 

(2)  Lime  may  be  combined  with  alumina  in  the  proportion  of  two  molecules 
to  one,  giving  a  product  which  sets  quickly  but  shows  good  hardening  proper- 
ties.    With  2  1  molecules  of  lime  to  one  of  alumina  the  product  is  unsound. 

Assuming  that  the  tricalcic  silicate  and  the  dicalcic  aluminate  are  the  most 
basic  compounds  which  can  exist  in  good  cement  we  arrive  at  the  following 
formula: 

,  SiO2)  +  F(2CaO,  A12O3), 


in  which  X  and  Y  are  variable  quantities  depending  upon  relative  proportions 
of  silica  and  alumina  in  materials  employed. 

3CaO,  SiO2  corresponds  to  2.8  parts  of  lime  by  weight  to  1  of  silica,  while 
2CaO,  A12O3  corresponds  to  1.1  parts  of  lime  to  one  of  alumina. 

Per  cent  lime  =  Per  cent  silicaX2.8+Per  cent  aluminaXl.l. 

Mr.  G.  A.  Rankin,  in  an  extended  study  of  the  composition  of 
Portland  cement2  finds  the  essential  constituents  to  be  the  trical- 
cium  silicate,  3CaO,  SiO2;  the  dicalcium  silicate,  2CaO,  SiO2;  and 
the  tricalcium  aluminate,  3CaO,  A12C>3.  He  finds  that  in  burning 
Portland  cement,  after  the  carbon  dioxide  has  been  driven  off,  the 
lime  combines  with  silica  and  alumina,  forming  first  a  fusible  alu- 
minate, 5CaO,  A1203,  and  the  dicalcium  silicate.  At  higher  tem- 
peratures these  compounds  unite  with  additional  lime,  forming  the 
tricalcium  aluminate  and  silicate.  When  the  material  is  not 
thoroughly  burned,  and  complete  equilibrium  is  not  reached,  the 
clinker  will  contain  free  lime,  CaO,  and  the  aluminate,  5CaO,  A12C>3. 
Magnesia  and  iron  oxide  have  little  influence  on  the  final  main 

1  Journal  Society  of  Chemical  Industry,  Nov.  30,  1897. 

2  Journal  Industrial  and  Engineering  Chemistry,  June,  1915. 


26  CEMENTING  MATERIALS 

constituents  of  the  cement,  but  act  as  fluxes  and  lower  the  temper- 
ature at  which  the  reactions  take  place. 

Too  high  proportion  of  lime  causes  cement  to  be  unsound  through 
the  presence  of  free  lime.  The  same  results  are  caused  by  under- 
burning  or  by  irregular  incorporation  of  the  raw  materials  into  the 
mixture.  As  perfect  uniformity  in  the  mixture  of  the  ingredients 
is  not  attainable  in  the  manufacture  of  cement,  it  is  necessary  that 
the  amount  of  lime  be  somewhat  less  than  the  theoretic  maximum 
to  avoid  unsoundness  in  the  cement.  The  desirable  proportion 
of  lime  seems  to  be  that  which  will  change  the  dicalcium  silicate 
to  tricalcium  silicate  as  completely  as  possible  without  producing 
unsoundness. 

The  ratio  of  silica  to  the  sum  of  alumina  and  iron  in  cement 
materials  is  known  as  the  silica  ratio.  It  is  desirable  that  the  silica 
ratio  be  at  least  2.5  or  possibly  3  in  Portland  cement. 

Very  little  is  definitely  known  concerning  the  chemical  reactions 
which  take  place  in  the  setting  and  hardening  of  cement  mortars. 
Studies  are  in  progress  which  it  is  hoped  may  throw  light  upon  the 
subject  and  tend  to  more  accurate  knowledge  of  the  requirements 
for  such  materials. 

ART.   6.     SPECIFICATIONS   AND   TESTS   FOR    CEMENT 

19.  Standard  Specifications. — The  specifications  of  the  American 
Society  for  Testing  Materials  are  now  commonly  recognized  as 
standard  and  used  in  the  purchase  of  cement  in  the  United  States. 
These  specifications  were  adopted  in  1904  and  revised  in  1908, 
1909,  and  1916.  In  specifications  for  construction  of  masonry  and 
concrete  it  is  usual  to  require  that  the  cement  meet  the  requirements 
of  the  American  Society  for  Testing  Materials,  although  in  ordinary 
work  it  is  not  common  to  actually  apply  all  the  tests.  The  tests 
of  chemical  analysis  and  specific  gravity  are  used  only  when  special 
reasons  exist  for  their  application  in  the  character  of  the  work  to 
which  the  cement  is  to  be  applied  or  doubt  as  to  the  material  offered. 

It  is  frequently  necessary,  on  important  work,  to  modify  the 
specifications  to  suit  the  peculiarities  of  the  particular  construction, 
This  is  particularly  the  case  in  work  to  be  subjected  to  the  action 
of  sea  water,  or  unusual  conditions  of  service. 

The  general  specifications  adopted  in  1909  were  modified  in  1916 
as  to  Portland  cement  only,  those  for  natural  cement  being  left 
unchanged.  The  Committee,  however,  expressed  the  intention  of 
proceeding  with  the  modification  of  the  requirements  for  natural 


SPECIFICATIONS  AND  TESTS  FOR  CEMENT  27 

cement  as  soon  as  possible,  and  changes  may  be  expected  in  these 
at  an  early  date.  The  methods  of  making  the  tests  for  Portland 
are  to  be  also  applied  to  natural  cement. 

The  1916  specifications  make  some  important  changes  from  those 
previously  used.  The  No.  100  sieve  is  dropped  from  the  test  for 
fineness  and  the  requirements  somewhat  increased  for  the  No.  200 
sieve.  The  Gillmore  needles  are  introduced  as  an  alternate  method 
in  the  test  for  rate  of  setting.  Tensile  tests  of  cement  paste  are 
dropped  and  sole  dependence  placed  on  the  1  to  3  mortar  test, 
requirements  for  which  are  somewhat  increased.  The  normal  test 
for  soundness  which  had  previously  been  the  final  test  is  dropped 
and  the  steam  test  is  made  the  standard. 

The  specifications  have  been  gradually  developed  through  experi- 
ence with  a  number  of  different  methods  of  testing  which  have  been 
changed  from  time  to  time  as  knowledge  of  the  material  has  increased 
and  manufacturers  have  improved  the  quality  of  the  material  they 
are  able  to  produce.  The  reliability  of  the  cement  on  the  market 
has  markedly  improved  within  a  few  years  past  and  the  likelihood 
of  finding  poor  cement  and  consequently  the  necessity  for  tests 
under  ordinary  circumstances  has  greatly  diminished.  The  applica- 
tion of  tests  where  feasible  and  upon  all  important  work  is,  however, 
desirable.  •  - ! 

The  specifications  for  Portland  cement  adopted  in  1916  are  the 
result  of  several  years'  work  of  a  Joint  Committee  of  the  American 
Society  of  Civil  Engineers,  the  U.  S.  Government  Engineers,  and 
the  American  Society  for  Testing  Materials.  They  are  published 
in  the  Book  of  Standards  of  the  Society  for  Testing  Materials,  and 
are  also  reprinted  for  distribution  to  those  interested  in  cement 
testing  by  the  Portland  Cement  Association. 

20.  Purpose  of  Standard  Tests. — The  tests  imposed  by  the 
standard  specifications  are  chemical  analysis,  specific  gravity,  fine- 
ness, normal  consistency,  time  of  setting,  tensile  strength,  and 
soundness.  Specifications  covering  all  of  these  are  usually  employed 
for  cement  to  be  used  in  important  work.  The  making  of  the  tests 
for  chemical  analysis  and  specific  gravity  are  often  omitted  when 
the  cement  proves  satisfactory  upon  the  other  tests. 

The  chemical  analyses  employed  for  Portland  cement  are  intended 
to  determine  whether  the  cement  has  been  adulterated  with  inert 
material,  such  as  slag  or  ground  limestone,  and  whether  magnesia 
or  sulphuric  anhydride  are  present  in  too  large  amounts. 

The  test  for  specific  gravity  when  used  for  Portland  cement  is 
intended  mainly  to  detect  adulteration  with  materials  of  lower 


28  CEMENTING  MATERIALS 

specific  gravity.  It  may  also  aid  in  determining  the  true  character 
of  the  material  and  whether  the  cement  is  well  burned.  The  specific 
gravity  of  Portland  cement  is  usually  between  3.10  and  3.20,  that 
of  a  natural  cement  2.75  to  3.10,  and  puzzolan  cement  2.7  to  2.9. 
Good  Portland  cement  may  be  lowered  in  specific  gravity  by  long 
exposure  to  the  air  without  serious  injury  to  the  cement.  For  this 
reason,  the  specifications  allow  a  second  test  upon  an  ignited  sample 
of  cement  failing  upon  a  first  test. 

The  test  for  normal  consistency  is  made  to  determine  the  proper 
quantity  of  water  to  be  used  in  the  paste  or  mortar  for  tests  of  time 
of  setting  or  strength.  In  the  preparation  of  paste  or  mortar  for 
these  tests,  variations  in  the  quantity  of  water  used,  or  in  the  methods 
of  mixing  and  molding  the  specimens,  may  produce  considerable 
differences  in  results.  A  standard  method  is  therefore  prescribed. 

The  time  of  setting  is  tested  for  the  purpose  of  determining  whether 
the  cement  is  suitable  for  a  given  use,  rather  than  as  a  measure  of 
the  quality  of  the  cement.  Testing  for  time  of  setting  consists  in 
arbitrarily  fixing  two  points  in  the  process  of  solidification  called 
the  initial  set  and  the  final  set.  This  is  accomplished  by  noting 
the  penetration  of  a  standard  needle  carrying  a  given  weight  into 
the  mass  of  cement. 

The  test  for  fineness  is  to  determine  whether  the  cement  is 
properly  ground.  Only  the  extremely  fine  powder  is  of  value  as 
cement.  The  coarse  parts,  while  having  some  cementing  value, 
are  practically  inert  when  used  in  sand  mortar. 

The  test  for  tensile  strength  of  cement  pastes  and  mortars  is  made 
for  the  purpose  of  demonstrating  that  the  cement  contains  the  active 
elements  necessary  to  cause  it  to  set  and  harden  properly.  Cement 
is  not  usually  subjected  to  tensile  stresses  in  use,  but  the  tensile 
test  has  commonly  been  employed  because  it  offers  the  easiest  way 
to  determine  strength,  and  seems  to  give  a  satisfactory  means  of 
judging  the  desired  qualities. 

The  proper  conduct  of  any  test  for  strength  is  a  matter  requiring 
care  and  experience.  There  are  a  number  of  points  connected  with 
the  conditions  and  manipulation  of  the  tests  which  have  important 
effects  upon  the  results.  These  are — the  form  of  the  briquette, 
the  method  of  mixing  and  molding,  the  amount  of  water  used  in 
tempering  the  mortar,  the  surroundings  in  which  the  mortar  is  kept 
during  hardening,  the  rate  and  manner  of  applying  the  stress,  the 
temperatures  at  which  all  the  operations  are  performed.  In  order 
to  secure  uniform  results,  it  is  essential  that  the  tests  be  standard- 
ized in  all  these  particulars. 


SPECIFICATIONS  AND  TESTS  FOR  CEMENT  29 

Soundness  is  the  most  important  quality  of  a  cement,  as  it  means 
the  power  of  the  cement  to  resist  the  disintegrating  influences  of 
the  atmosphere  or  water  in  which  it  may  be  placed.  Unsoundness 
in  cement  may  vary  greatly  in  degree,  and  show  itself  quite  dif- 
ferently in  different  material.  Cement  in  which  unsoundness  is 
very  pronounced  is  apt  to  become  distorted  and  cracked  after  a  few 
days,  when  small  cakes  are  placed  in  water.  Those  in  which  the 
disintegrating  action  is  slower  may  not  show  any  change  of  form, 
but  after  weeks  or  months  gradually  lose  coherence  and  soften  until 
entirely  disintegrated. 

The  object  in  the  tests  is  to  accelerate  the  actions  which  tend 
to  destroy  the  strength  and  durability  of  the  cement.  As  the  tests 
must  be  made  in  a  short  time,  it  is  necessary  to  handle  the  cement 
in  such  manner  as  to  cause  these  qualities  to  show  quickly. 

Normal  Test. — The  method  which  has  been  commonly  employed 
is  to  make  small  cakes,  or  pats,  of  cement  paste  about  3  inches  in 
diameter  and  \  inch  thick  at  the  center,  with  thin  edges,  upon  a 
plate  of  glass  about  4  inches  square.  These  pats  are  kept  twenty- 
four  hours  in  moist  air  and  then  allowed  to  stand  for  twenty-eight 
days  in  water,  or  in  the  air.  The  pat  during  this  period  should  show 
no  signs  of  cracking,  checking,  distortion,  or  disintegration.  This 
is  known  as  the  normal  test,  and  has  been  relied  upon  as  the  final 
test  for  soundness.  This  test  is  defective  in  requiring  too  much 
time  and  also,  in  some  instances,  fails  to  discover  defective  material 
in  which  the  action  is  very  slow. 

Accelerated  Tests. — Numerous  tests  have  been  proposed  for  the 
purpose  of  hastening  the  hardening  of  the  cement  and  causing 
unsoundness  to  show  more  quickly.  In  most  of  these  tests,  heat 
is  employed  to  accelerate  the  changes  taking  place  in  the  cement, 
and  they  are  known  as  accelerated  tests. 

These  tests  have  usually  been  made  by  subjecting  small  pats 
of  the  cement  to  the  action  of  hot  water  or  steam  and  observing 
whether  cracking  or  disintegration  takes  place.  Sometimes  small 
bars  of  cement  are  used  and  the  increase  in  length  of  the  bar  meas- 
ured after  exposure  to  the  hot  water  or  steam.  The  expansion  of 
unsound  cement  should  be  much  greater  than  that  of  sound  cement. 
The  tensile  strengths  of  briquettes  of  cement  which  have  been  exposed 
to  hot  water  or  steam  are  sometimes  measured  and  compared  with 
the  strengths  of  similar  briquettes  kept  at  normal  temperatures. 
The  heat  should  cause  a  considerable  increase  in  strength  of  sound 
cement. 

The  standard  steam  test  consists  in  observing  the  effect  of  steam 


30  CEMENTING  MATERIALS 

at  about  100°  C.  upon  small  pats  of  the  cement.  This  test  was 
recommended  by  a  committee  of  the  American  Society  of  Civil 
Engineers  in  1904.  It  has  since  been  included  in  the  specifications 
of  the  American  Society  for  Testing  Materials  in  conjunction  with 
the  normal  pat  test,  which  was  the  deciding  test.  In  the  modified 
specifications  for  Portland  cement  adopted  in  1916,  the  normal 
test  is  discontinued  and  the  steam  test  becomes  the  standard. 

The  methods  for  making  the  standard  tests  are  described  in 
detail,  with  the  specifications,  in  the  Book  of  Standards  of  the 
American  Society  for  Testing  Materials,  and  in  the  reprint  pub- 
lished by  the  Portland  Cement  Association. 

21.  Tests    of    Compressive    Strength. — Tests    of    compressive 
strength  are  seldom  used  in  specifications  for  cement,  on  account 
of  the  greater  ease  of  making  the  tensile  test  and  the  lighter  machines 
that  may  be  employed  for  the  purpose.     These  tests  have  frequently 
been  made  for  purposes  of  comparison  or  to  determine  special  qualities 
of  the  material.     The  standard  test  piece  has  usually  been  a  2-inch 
cube,  prepared  in  the  same  manner  as  the  tension  specimens.     This 
was  recommended  by  a  committee  of  the  American  Society  of  Civil 
Engineers  in  1909. 

As  cement  mortar  is  usually  employed  in  compression,  some 
engineers  prefer  to  use  the  compression  test  in  their  specifications. 
A  new  tentative  specification  with  methods  of  testing  was  recom- 
mended by  a  committee  of  the  American  Society  for  Testing  Materi- 
als in  1916.  This  has  not  been  adopted  by  the  society  as  a  standard, 
and  may  be  further  modified  before  such  adoption.  It  is  probable 
that  such  a  standard  will  be  adopted,  to  be  used  in  conjunction 
with  or  to  replace  the  tension  test.  This  proposed  specification 
with  the  method  of  making  the  test  is  given  in  Volume  I  of  the 
Transactions  of  the  Society  for  1909.  Reprints  may  be  had  from 
the  Secretary  of  the  Society. 

22.  Special  Tests. — The  tests  ordinarily  employed  in  determin- 
ing the  quality  of  cement  are  enumerated  in  the  preceding  sections. 
Other  tests  are  frequently  made  to  determine  special  qualities  or 
for  the  purpose  of  investigating  properties  of  cements  and  mortars. 

Transverse  Strength. — Tests  of  the  strength  of  cement  mortar 
under  transverse  loading  are  seldom  employed  as  a  measure  of  the 
quality  of  the  material,  but  are  frequently  made  with  a  view  to 
determining  the  action  of  the  material  in  service.  Propositions 
have  often  been  made  to  substitute  the  transverse  for  the  tensile 
test  in  the  reception  of  material.  These  suggestions  have  usually 
been  based  upon  the  simplicity  of  the  test  and  of  the  apparatus 


SAND  FOR   MORTAR  31 

with  which  it  may  be  carried  out.  The  specimen  usually  employed 
for  this  purpose  is  1  inch  by  1  inch  and  6  inches  long.  It  is  tested 
by  placing  upon  knife  edges  5  inches  apart  and  bringing  the  load 
upon  the  middle  section.  Professor  Durand-Claye,  from  a  large 
number  of  comparative  tests,  found  the  unit  fiber  stress  under 
transverse  load  to  average  about  1.9  times  the  unit  stress  for  tension. 

Adhesive  Strength. — The  ability  of  cement  mortar  to  adhere 
firmly  to  a  surface  with  which  it  may  be  placed  in  contact  is  one 
of  its  most  valuable  properties  and  quite  as  important  as  the  develop- 
ment of  cohesive  strength.  Tests  for  adhesive  strength  are  not 
employed  as  a  measure  of  quality, .  because  of  the  uncertain  char- 
acter of  the  test  and  the  difficulty  of  so  conducting  it  as  to  make 
it  a  reliable  indication  of  value.  The  adhesive  properties  of  the 
cement  are  to  a  certain  extent  called  into  play  in  tests  of  sand  mor- 
tar, and  may  be  inferred  from  comparison  of  neat  and  sand  tests. 

Experiments  upon  the  adhesion  of  mortars  to  various  substances 
are  sometimes  made,  both  for  the  purpose  of  comparing  the  cements 
or  methods  of  use,  and  to  study  the  relative  adhesions  to  various 
kinds  of  surfaces.  Such  experiments  are  quite  desirable  with  a 
view  to  the  extension  of  knowledge  of  this  very  important  quality. 

The  common  method  of  making  this  test  is  to  prepare  briquettes 
of  which  one  half  the  briquette  is  of  cement  paste  or  mortar  and  the 
other  half  a  block  of  stone,  glass,  or  other  material  to  be  used.  The 
cement  half  is  made  in  the  ordinary  form  for  tensile  specimens. 
The  other  half  is  made  to  fit  the  cement  mold  at  the  middle  and 
arranged  at  the  end  to  be  held  by  a  clip  in  the  testing  machine. 

ART.   7.     SAND   FOR  MORTAR 

23.  Quality  of  Sand. — As  hydraulic  cement  is  commonly  mixed 
with  certain  proportions  of  sand,  when  used  in  construction,  the 
nature  and  quality  of  sand  used,  and  the  method  of  manipulating 
the  materials  in  forming  the  mortar  have  quite  as  important  an 
effect  upon  the  final  strength  of  the  work  as  the  quality  of  the  cement 
itself. 

In  testing  cement  a  standard  sand  is  employed.  This  sand  may 
be  obtained  quite  uniform  in  quality.  In  the  execution  of  work, 
however,  local  sand  must  generally  be  used;  this  varies  widely  in 
character,  and  should  always  be  carefully  considered  upon  any 
work  where  the  development  of  strength  and  lasting  qualities  are 
of  importance. 

Size  of  Sand  Grains. — It  is  usual  to  class  as  sand  all  material 


32  CEMENTING  MATERIALS 

less  than  J-inch  diameter;  pieces  larger  than  this  being  classed  as 
gravel.  Coarse  sand  is  superior  to  fine  sand  for  use  in  cement 
mortar.  Coarse  sand  presents  less  surface  to  be  coated  with  cement 
and  the  interstices  are  more  easily  filled  with  cement  paste.  Fine 
sand  requires  more  water  in  mixing  to  the  same  consistency,  and 
gives  usually  weaker  and  more  porous  mortar  than  coarse  sand. 

The  use  of  a  mixture  of  grains  of  different  sizes  is  usually  desir- 
able, giving  less  voids  to  be  filled  by  the  cement;  and  it  is  frequently 
found,  when  the  cement  is  not  in  considerable  excess,  that  .the 
strength  obtained  by  such  a  mixture  is  much  greater  than  is  given 
by  either  the  large  or  small  grains  alone.  Sand  of  mixed  sizes, 
giving  a  minimum  of  voids,  requires  less  cement  to  make  a  mortar 
of  maximum  density  and  strength  than  that  of  more  uniform  sizes. 

Shape  of  Grains. — Sand  with  angular  grains  usually  gives  better 
results  in  mortar  than  that  with  rounded  grains,  and  specifications 
frequently  call  for  sharp  sand.  This  difference  is,  however,  much 
less  important  than  that  of  proper  gradation  of  sizes,  and  should 
not  be  given  undue  weight  in  the  selection  of  sand  for  use  in  mortar. 

Stone  Screenings. — The  screenings  from  crushed  stone  are  fre- 
quently used  in  place  of  natural  sand.  Ordinarily  screenings  from 
stone  of  good  quality  give  mortar  of  rather  better  strength  than 
natural  sand.  This,  however,  depends  in  most  instances  upon  the 
gradation  of  sizes  in  the  two  materials.  The  sharpness  of  grain 
is  favorable  to  the  screenings,  and  the  presence  of  a  certain  amount 
of  very  fine  stone  dust  in  the  screenings  seems  to  be  of  value  in  the 
mortar.  When  the  screenings  are  derived  from  soft  rock,  the  dust 
may  be  present  in  too  large  amount  and  need  to  be  screened  out 
before  the  screenings  can  be  successfully  used. 

Chemical  Composition. — Sands  as  commonly  used  for  mortar  are 
composed  mainly  of  silica.  In  most  cases,  sand  which  has  a  proper 
granulometric  composition  is  satisfactory  for  use.  The  failure  of 
concrete  work  has,  however,  in  a  number  of  instances  been  found 
to  be  due  to  the  use  of  sand  low  in  silica.  Sand  containing  less  than 
95  per  cent  silica  needs  to  be  carefully  tested  before  being  used, 
although  some  sands  as  low  as  75  per  cent  silica  have  given  good 
results.  The  composition  of  sands  have  not  been  sufficiently  studied 
to  determine  the  differences  of  composition  which  cause  failure  in 
one  case  and  success  in  another. 

The  presence  of  mica  in  sand  or  screenings  is  supposed  to  injuri- 
ously affect  the  strength  of  mortar  in  which  the  material  is  used. 
The  results  of  experiments  upon  the  effect  of  mica  are  not  conclusive, 
although  they  seem  to  indicate  that  mica  may  sometimes  be  injuri- 


SAND  FOR  MORTAR  33 

ous.  Sand  containing  mica  should  be  carefully  tested  before  being 
used. 

Effect  of  Impurities. — Sand  for  use  in  mortar  should  be  clean,  and 
as  free  from  loam,  mud,  or  organic  matter  as  possible.  In  general 
the  presence  of  any  foreign  matter  is  to  be  avoided,  though  a  small 
amount  of  fine  clay  distributed  through  sand  has  sometimes  been 
found  to  increase  the  strength  of  cement  mortar,  and  also  helps  to 
make  the  mortar  work  more  smoothly,  sometimes  decreasing  its 
permeability.  The  effect  of  the  clay  depends  upon  the  character 
of  the  sand  and  upon  the  richness  of  the  mortar.  Fine  clay  may 
help  to  fill  the  voids  in  an  otherwise  porous  mortar  with  good  effect, 
but  may  be  deleterious  in  a  rich  mortar,  or  when  it  is  not  finely  divided 
and  uniformly  distributed  through  the  sand.  In  a  particular  instance, 
the  effect  of  such  an  adulteration  can  be  judged  only  by  testing  it. 

Impurities  of  an  organic  nature  are  always  objectionable  in  sand 
for  use  in  mortar.  When  it  is  necessary  to  use  sand  containing 
such  impurities,  it  should  be  carefully  washed  and  tested.  A  very 
small  amount  of  vegetable  matter  in  sand  has  sometimes  caused 
the  failure  of  mortar  to  harden  properly. 

Selection  of  Sand. — Sands  differ  so  greatly  in  their  qualities  that 
it  is  difficult  by  mere  inspection  of  the  materials  to  judge  of  their 
relative  values  for  use  in  mortar.  In  choosing  sand  for  use  in  impor- 
tant work,  it  is  desirable  not  only  to  determine  fully  the  physical 
characteristics  of  the  available  materials,  but  also  to  make  actual 
tests  of  mortar  by  their  use. 

24.  Tests  for  Sand. — Tests  intended  to  determine  the  mortar- 
making  qualities  of  sand  may  be  made  in  three  ways: 

1.  Mechanical  analysis  of  the  sand,  with  determination  of  voids 
in  the  sand. 

2.  Density  tests  of  mortars  made  from  the  sand  with  the  cement 
to  be  used  in  the  work. 

3.  Strength  tests  of  mortars  made  from  the  sand  in  question  with 
the  cement  to  be  used  hi  the  work. 

The  value  of  sand  depends  mainly  upon  its  granulometric  com- 
position. The  sand  which,  mixed  with  a  given  proportion  of  cement, 
gives  the  most  dense  mortar  yields  the  strongest  mortar.  The  sand 
which  requires  the  least  cement  to  make  a  mortar  of  maximum 
density  is  the  most  economical  sand,  when  the  mortar  is  properly 
proportioned. 

The  purpose  in  testing  the  sand  should  be  to  determine  the  pro- 
portions of  cement  to  sand  necessary  as  well  as  to  choose  the  best 
sand. 


34  CEMENTING  MATERIALS 

25.  Mechanical  Analysis. — To  determine  the  relative  sizes  of  grains 
composing  sand,  the  material  is  screened  through  a  series  of  sieves 
of  varying  degrees  of  fineness.  The  sieves  are  made  of  standard 
size,  8  inches  in  diameter  by  2J  inches  high,  those  with  openings 
smaller  than  ^  inch  being  made  of  woven  brass  wire,  while  the  larger 
sizes  are  preferably  drilled  circular  openings  in  sheet  brass.  These 
sieves  are  designated  by  numbers  corresponding  to  the  number  of 
meshes  to  the  linear  inch,  the  size  of  opening  depending  upon  the 
diameter  of  wire  used.  The  size  openings  usually  employed  for 
sand  analysis  are  approximately  as  follows : 

No.  of  Sieve 4       10        20        30        40        50        80       100        200 

Size  Opening,  in. ..   0.25  .073    .0335   .0195    .015     .011    .0067  .0055    .00265 

For  ordinary  examination  of  sand,  when  comparing  or  selecting 
sand  for  use,  it  is  unnecessary  to  separate  into  so  many  sizes,  and 
sieves  Nos.  4,  10,  20,  50,  and  100  are  commonly  employed.  The 
sieves  are  made  to  fit  together  in  nests  with  a  cover  and  tight  bottom 
to  catch  the  residue  from  the  finest  sieves.  The  sifting  may  be  done 
by  hand,  by  shaking  and  jarring  the  sieves,  or  mechanical  shakers 
may  be  used.  These  may  be  obtained  to  work  by  hand  or  with 
small  electric  motors  attached. 

In  making  the  tests,  a  sample  weighing  50  g.  is  dried  to  constant 
weight  at  temperature  not  more  than  110°  C.  (230°  F.)  and  is  then 
sifted  through  the  sieves,  so  as  to  separate  the  grains  into  various 
sizes  and  determine  the  percentage  of  each  by  weight.  The  material 
properly  classed  as  sand  is  that  which  passes  through  the  No.  4 
sieve  and  is  retained  on  the  No.  100  sieve.  Sand  retained  by  the 
No.  10  or  No.  20  sieve  may  be  classed  as  coarse  sand;  that  caught 
between  the  No.  20  and  No.  50  sieves  is  medium  sand;  that  which 
passes  the  No.  50  sieve  is  fine  sand.  Material  passing  the  No.  100 
sieve  is  called  dust. 

Analysis  Curves. — Comparisons  of  the  granulometric  composi- 
tions of  sands  are  readily  made  by  plotting  the  results  of  the  sieve 
analysis  as  curves.  It  is  usual  to  plot  the  sizes  of  openings  as  abscissae 
and  percentages  passing  each  size  as  ordinates.  The  reciprocals 
of  the  numbers  of  the  sieves  may  be  used  for  size  without  impairing 
the  value  of  the  results,  and  probably  represent  more  nearly  the 
actual  sizes  of  grains  passing  the  sieves  than  does  the  computed 
width  of  opening.  Table  II  gives  the  results  of  analyses  of  sands 
in  common  use  for  mortar,  showing  something  of  the  variations 
which  may  frequently  occur. 

These  results  are  plotted  in  Fig.  1.     Sand  No.  1  is  a  coarse  bank 


SAND    FOR   MORTAR 


35 


sand  containing  a  small  amount  of  clay.  No.  2  is  a  medium  river 
sand  of  good  quality.  No.  3  is  a  fine  sand.  No.  4  is  screenings 
from  broken  limestone,  containing  rather  high  percentage  of  dust. 

TABLE  II.— ANALYSES  OF  SANDS 


PERCENTAGES  PASSING  SIEVES. 

Sieve  No. 

Sand. 

Screenings. 

1 

2 

3 

4 

4 

100 

100 

100 

100 

10 

57.82 

85.18 

99.82 

95.07 

20 

34.96 

56.82 

99.42 

74.01 

30 

10.00 

33.93 

97.33 

59.68 

40 

7.67 

20.02 

83.74 

49.23 

50 

5.82 

13.07 

35.13 

41.91 

80 

3.69 

7.44 

2.27 

30.97 

100 

3.01 

5.18 

0.96 

28.24 

200 

1.73 

0.38 

0.65 

17.71 

100 


.Ol     .02.    .03   .04, .05    .06    .07    .08    .09    .10    .11     .IE 
51ZEOF  OPENING  IN  INCHE5 

FIG.  1. — Analyses  of  Sands. 


36  CEMENTING   MATERIALS 

26.  Determination  of  Voids.  —  The  method  most  commonly  used 
for  void  determination  is  known  as  the  wet  method,  which  consists 
in  filling  a  measure  with  the  sand  to  be  tested  and  pouring  in  water 
until  the  voids  are  completely  filled.  The  volume  of  water  required 
to  fill  the  voids  divided  by  the  volume  of  sand  and  multiplied  by 
100  is  the  percentage  of  voids;  or  the  weight  of  water  poured  into 
the  sand  divided  by  the  weight  of  water  required  to  fill  the  measure 
and  multiplied  by  100  is  the  percentage  of  voids.  It  is  very  dif- 
ficult to  eliminate  completely  the  air  from  the  sand  in  making  this 
test.  The  test  is  therefore  liable  to  considerable  error  unless  great 
care  be  used  in  manipulating  it. 

Dry  Method.  —  A  more  accurate  method  of  determining  voids 
is  to  compare  the  weight  of  a  measured  volume  of  the  sand  with 
the  weight  of  an  equal  volume  of  the  solid  material  of  which  the 
sand  is  composed.  In  measuring  the  volume  of  sand,  it  is  necessary 
to  use  care  to  secure  the  proper  degree  of  compactness.  For  ordi- 
nary comparisons  the  sand  should  be  well  compacted  by  shaking 
and  jarring  the  measure.  The  weight  of  the  solid  rock  is  obtained 
by  multiplying  the  weight  of  an  equal  volume  of  water  by  the  specific 
gravity  of  the  sand.  The  difference  between  the  weight  of  the 
rock  and  that  of  the*  sand  divided  by  the  weight  of  the  rock  and 
multiplied  by  100  is  the  percentage  of  voids. 

If  R  is  the  weight  of  the  solid  rock  and  S,  the  weight  of  the  sand, 
percentage  of  voids  is 


This  test  supposes  the  sand  to  be  dry.  When  it  is  desired  to 
obtain  the  voids  in  moist  sand,  a  weighed  sample  of  the  sand  should 
be  dried  at  212°  F.  and  the  loss  of  weight  determined.  The  weight 
of  moisture  in  the  measure  of  sand  to  be  used  in  the  test  may  then 
be  computed.  This  weight  is  then  to  be  subtracted  from  the  total 
weight  of  the  moist  sand  to  find  the  weight  of  solid  material  in  the 
sand. 

If  m  is  the  weight  of  moisture  in  the  volume  of  sand  under  test, 
percentage  of  voids  is 

R-(S-m). 


R 


100. 


27.  Specific  Gravity. — The  specific  gravity  of  siliceous  sand  is 
quite  uniformly  2.65,  or  the  weight  per  cubic  foot  of  the  solid  rock 
is  165  pounds.  To  assume  these  values  in  determining  the  voids 


SAND  FOR   MORTAR 


37 


in  such  sand  involves  slight  error  in  any  case.  Sands  not 
strictly  siliceous  may  vary  in  specific  gravity  from  about  2.6 
to  2.7. 

The  determination  of  specific  gravity  is  made  by  immersing  a 
sample  of  the  material  in  water  at  68°  F.  and  dividing  the  weight 
of  the  sand  by  the  weight  of  water  displaced.  This  is  most  con- 
veniently done  by  sifting  the  sand  into  the  water  in  a  graduated 
glass  tube,  and  reading  the  increase  of  volume  of  the  liquid  in  the 
tube.  Care  must  be  used  to  introduce  the  sand  slowly  so  as  to 
eliminate  all  air  bubbles. 

28.  Density  Test. — Comparative  tests  of  sands  may  be  made 
by  determining  the  volume  of  mortar  produced  by  definite  weights 
of  cement  and  dry  sand.  The  sand  that  for  a  given  weight  of  materi- 
als, when  mixed  with  the  same  proportion  of  cement  to  the  required 
consistency,  produces  the  smallest  volume  of  mortar  gives  the  most 
dense  mortar.  In  making  this  test,  molds  in  which  the  height  is 
large  in  comparison  with  the  section  are  convenient,  the  relative 
heights  to  which  the  mold  is  filled  giving  the  proportionate  volumes. 
The  volume  of  mortar  after  setting  is  what  is  required,  but  the 
measurement  before  setting,  unless  the  mortar  is  quite  wet,  will  give 
practically  the  same  result. 

Determination  of  Density. — The  term  density,  as  commonly 
applied  to  mortar,  means  the  ratio  of  the  volume  of  solid  materials 
contained  in  the  mortar  to  the  whole  volume  of  mortar.  The  density 
is  obtained  by  weighing  the  ingredients  before  mixing  and  calculating 
their  solid  volumes  from  these  weights  and  their  specific  gravities. 
The  weight  and  volume  of  the  resulting  mortar  are  then  measured. 
The  weight  of  mortar  should  equal  the  sum  of  the  weights  of  the 
several  ingredients.  The  density  equals  the  sum  of  the  solid  vol- 
umes of  sand  and  cement  divided  by  the  measured  volume  of  the 
mortar.  The  density  of  mortars  made  from  the  sands  shown  in 
Fig.  1,  one  part  cement  to  three  parts  sand  by  volume,  are  as 
follows : 


WEIGHTS  USED,  GRAMS. 

Mortar 

Sand  No. 

Cement. 

Sand. 

Water. 

c.c. 

1 

358 

1026 

178 

670 

0.75 

2 

358 

1128 

163 

735 

0.73 

3 

358 

972 

180 

730 

0.66 

4 

358 

1122 

268 

790 

0.68 

38 


CEMENTING  MATERIALS 


The  method  of  computation  is  as  follows: 

Taking  specific  gravity  of  cement  as  3.1  and  specific  gravity 
of  sand  as  2.65, 


Density  of  No.  1  is 


358     1026 
3.1     2 . 65  _ 
670 


29.  Strength  Tests. — Tests  of  the  strength  of  mortars  made 
from  sands  are  the  most  conclusive  evidence  of  the  mortar-making 
properties  of  the  sands.  These  tests  to  be  of  real  value  should 
extend  over  a  period  of  at  least  twenty-eight  days.  They  are  made 
in  the  same  manner  as  the  mortar  tests  for  judging  cement,  and 
comparisons  are  sometimes  made  with  the  results  of  tests  with 
standard  sand.  Table  III  gives  comparative  results  of  tests  of  the 
sands  shown  in  Fig.  1. 


TABLE  III.— RESULTS  OF  SAND  TESTS 


Sand  No. 

PACKED  SAND. 

Density, 
1  :3 
Mortal  . 

TENSILE  STRENGTH. 

Per  Cent 
Voids. 

Weight, 
Cu.  Ft. 

1  :  2  Mortar. 

1  :  3  Mortar. 

28  Days. 

6  Months. 

28  Days. 

6  Months. 

1 

2 
3 

4 
Standard.  . 

36.1 

28.6 
38.0 

28.7 

106.4 
117.5 
100.8 
116.7 

.75 
.73 

.66 
.68 

523 
379 
223 
396 
326 

603 
493 
343 
567 

477 

443 
253 
153 

304 

268 

495 
339 
265 
503 
318 

30.  Washing  Test. — When  it  is  necessary  to  examine  sand  for 
organic  impurities,  the  silt  may  be  removed  from  the  sand  by  washing. 
This  is  done  by  shaking  a  sample  of  the  sand  in  a  bottle  with  water, 
letting  it  settle  for  a  few  seconds,  and  then  pouring  off  the  turbid 
water.  This  is  done  repeatedly  until  the  suspended  matter  is  all 
removed.  The  wash  water  is  then  evaporated,  and  the  amount 
of  silt  determined. 

The  silt  is  ignited  in  a  platinum  crucible  and  the  loss  on  ignition 
is  the  percentage  of  organic  matter  present. 

A  very  small  amount,  not  more  than  1  per  cent,  of  organic  matter 
may  be  a  serious  detriment,  sand  containing  such  impurities  should 
be  carefully  tested  and  may  need  to  be  washed  in  order  to  give  satis- 
factory results  in  use. 


CEMENT   MORTAR  39 

31.  Specifications  for  Sand. — Tests  have  seldom  been  used  as 
means  of  judging  sand  for  use  in  masonry  construction.  The  require- 
ments have  usually  been  that  the  sand  be  coarse,  clean,  and  sharp; 
the  requirement  of  sharpness  is  now  commonly  omitted. 

Mechanical  analysis  and  void  tests  are  frequently  made  for  the 
purpose  of  judging  the  qualities  of  available  sands  on  important 
work,  and  to  aid  in  properly  proportioning  mortar,  but  such  tests 
are  not  usual  in  specifications. 

The  Joint  Committee  of  the  Engineering  Societies  on  Concrete 
and  Reinforced  Concrete  has  suggested  the  following  as  requirements 
for  sand  to  be  used  as  fine  aggregate  in  concrete  work: 

(a)  Fine  Aggregate. — This  should  consist  of  sand,  crushed  stone  or  gravel 
screenings,  graded  from  fine  to  coarse,  and  passing  when  dry  a  screen  having 
holes  i  inch  in  diameter.  It  is  preferable  that  it  be  of  siliceous  material,  and 
should  be  clean,  coarse,  free  from  dust,  soft  particles,  vegetable  loam,  or  other 
deleterious  matter;  and  not  more  than  6  per  cent  should  pass  a  sieve  having 
100  mashes  per  linear  inch.  Fine  aggregates  should  always  be  tested. 

Fine  aggregates  should  be  of  such  quality  that  mortar  composed  of  one  part 
Portland  cement  and  three  parts  fine  aggr  gates  by  weight,  when  made  into 
briquettes,  will  show  a  tensile  strength  at  least  equal  to  the  strength  of  1  to  3 
mortar  of  the  same  consistency  made  with  the  same  cement  and  standard  Ottawa 
sand.  If  the  aggregate  be  of  poorer  quality,  the  proportion  of  cement  should 
be  increased  to  secure  the  desired  strength. 

If  the  strength  developed  by  the  aggregate  in  the  1  to  3  mortar  is  less  than 
70  per  cent  of  the  strength  of  the  Ottawa  sand  mortar,  the  material  should  be 
rejected.  To  avoid  the  removal  of  any  coating  on  the  grains,  which  may  effect 
the  strength,  bank  sand  should  not  be  dried  before  being  made  into  mortar, 
but  should  contain  natural  moisture.  The  percentage  of  moisture  may  be 
determined  on  a  separate  sample  for  correcting  weight.  From  10  to  40  per  cent 
more  water  may  be  required  in  mixing  bank  or  artificial  sands  than  for  standard 
Ottawa  sand  to  produce  the  same  consistency. 


ART.   8.     CEMENT  MORTAR 

32.  Proportioning  Mortar. — In  specifying  the  proportions  of 
ingredients  for  cement  mortar  to  be  used  in  construction,  it  is  usual 
to  give  the  ratio  of  parts  of  cement  to  those  of  sand  by  volume 
The  relative  proportions  of  sand  and  cement  to  be  used  in  any 
instance  depend  upon  the  nature  of  the  work  and  the  necessity  for 
developing  strength  or  water-tightness  in  the  mortrr.  The  pro- 
portions commonly  used  in  ordinary  work  are:  for  natural  cement, 
one  part  cement  to  one  part  or  two  parts  sand;  for  Portland  cement, 
one  part  cement  to  two  parts  or  three  parts  of  sand.  In  common 
practice  these  ratios  are  chosen  without  reference  to  the  particular 
materials  used  and  the  resulting  mortars  vary  widely  in  character. 


40  CEMENTING  MATERIALS 

Good  sand  in  a  i  to  3  mortar  frequently  shows  greater  strength 
than  a  poorer  one  mixed  1  to  2,  and  gives  equally  good  results  in 
use. 

The  methods  of  measuring  materials  also  vary,  and  the  relative 
quantities  of  cement  and  sand  in  the  mortar  differ  correspondingly. 

Measuring  Cement. — Cement  should  always  be  measured  by 
weight,  on  account  of  the  variation  in  volume  of  the  same  quantity 
of  cement  with  different  degrees  of  compactness.  In  specifying 
proportions  by  volume,  therefore,  it  is  always  desirable  to  state 
the  weight  of  cement  to  be  taken  as  unit  volume. 

Portland  cement  is  usually  packed  in  wooden  barrels  or  in  canvas 
bags.  A  barrel  of  cement  contains  376  pounds  of  cement,  while 
a  bag  contains  94  pounds,  or  one-quarter  barrel.  Natural  cement 
is  ordinarily  packed  in  barrels  of  282  pounds,  or  bags  of  94  pounds 
(one-third  barrel)  each. 

Portland  cement  as  packed  in  barrels  weighs  a  little  more  than 
100  pounds  per  cubic  foot.  A  cubic  foot  of  cement  paste  requires 
from  95  to  110  pounds  of  cement.  It  is  common  to  consider  a  cubic 
foot  of  Portland  cement  to  weigh  94  pounds  in  porportioning  mortar. 
A  bag  of  cement  is  then  mixed  with  2  cubic  feet  of  sand  to  form 
1  to  2  mortar,  or  with  3  cubic  feet  of  sand  to  form  1  to  3  mortar. 
This  assumes  the  volume  of  a  barrel  of  cement  to  be  4  cubic  feet. 
This  is  the  recommendation  of  the  Joint  Committee  of  the  Engineer- 
ing Societies.  Some  engineers  use  3.8  cubic  feet  as  the  volume  of 
a  barrel,  or  100  pounds  as  the  weight  of  a  cubic  foot. 

In  the  same  way,  70  pounds  is  frequently  used  as  the  weight  of 
a  cubic  foot  of  natural  cement.  This  makes  the  volume  of  a  sack 
of  natural  cement  1J  cubic  feet.  A  barrel  of  natural  cement  would 
then  have  the  same  nominal  volume  as  a  barrel  of  Portland,  4  cubic 
feet.  The  actual  volume-weight  of  natural  cement  varies  con- 
siderably for  different  brands. 

Measuring  Sand. — It  is  usual  to  measure  sand  by  volume.  The 
method  of  measuring  to  be  used  in  any  particular  instance  depends 
upon  the  method  of  mixing  and  handling  the  mortar.  Very  com- 
monly the  measuring  is  done  in  the  barrow  or  bucket  in  which  the 
sand  is  carried  to  the  mixer  or  platform.  Measuring  boxes  with- 
out bottoms  are  often  employed  to  set  on  the  mixing  platform,  and 
after  filling  are  removed,  leaving  the  measure  of  sand.  Whatever 
method  of  handling  the  sand  is  employed,  it  is  important  that  care- 
ful attention  be  given  to  securing  the  correct  proportion  of  sand 
for  the  mortar. 

Effect  of  Moisture. — In   proportioning   mortar  by   volume,   the 


CEMENT   MORTAR  41 

moisture  content  of  the  sand  may  be  a  matter  of  importance.  Damp 
sand  weighs  less  per  unit  volume  than  dry  sand.  When  sand  is 
moistened  with  a  small  quantity  of  water,  the  grains  of  sand  are 
coated  with  a  thin  film  of  water,  which  separates  the  grains,  causing 
the  sand  to  occupy  more  space  than  when  dry.  When  the  amount 
of  water  becomes  sufficient  to  coat  all  the  grains  of  sand  (about 
4  to  7  per  cent  with  ordinary  sands),  a  maximum  effect  is  reached, 
and  an  increase  in  amount  of  water  beyond  that  point  causes  a  reduc- 
tion of  volume.  At  saturation  (10  to  20  per  cent  of  water),  it  becomes 
slightly  less  in  volume  than  when  dry. 

The  solid  content  in  a  given  volume  of  moist  sand  is  less  than 
that  of  the  same  volume  of  dry  sand,  and  a  mortar  mixed  with  the 
moist  sand  will  be  richer  in  cement  than  that  mixed  with  the  same 
sand  when  dry.  This  effect  is  greater  with  fine  then  with  coarse 
sand.  A  given  volume  of  sand  measured  dry  may  contain  10  per 
cent  to  15  per  cent  more  solid  material  than  the  same  volume  of 
the  same  sand  measured  in  a  moist  condition. 

The  extent  to  which  differences  in  moisture  condition  may  effect 
the  volume  of  the  sand  depends  upon  the  position  in  which  the  sand 
is  placed  and  the  way  it  is  handled  in  measuring.  If  dry  sand  in 
a  bin,  or  a  pile,  be  moistened  with  a  small  quantity  of  water,  the 
sand  will  not  appreciably  swell  in  the  pile,  as  the  particles  are  held 
by  the  weight  of  the  mass  above — they  are  not  free  to  move  and  the 
water  fails  to  separate  them.  If  the  sand  be  loosened  in  moving 
to  a  new  position,  it  will  be  found  to  have  increased  in  volume  and 
will  not  return  to  its  former  dimensions  until  it  has  become  dry, 
or  wet  to  saturation. 

Proportioning  by  Weight. — In  Germany  it  has  been  quite  common 
to  measure  the  material  for  mortar  by  weight.  This  has  been  applied 
in  some  instances  in  the  United  States,  and  reduces  largely  the  vari- 
ations in  the  proportions  due  to  moisture.  On  important  work  it 
may  frequently  be  possible  to  arrange  for  weight  measurement 
without  materially  increasing  the  cost  of  handling  the  material. 

The  ratio  of  cement  to  sand  is  commonly  arbitrarily  fixed  with 
reference  to  the  particular  use  to  which  the  mortar  is  to  be  put, 
without  considering  the  character  of  the  sand  to  be  used.  For 
ordinary  masonry,  or  massive  concrete,  Portland  cement  is  usually 
employed  in  1  to  3  mixtures.  When  high  strength  is  needed,  as 
in  reinforced  concrete  work,  the  mixture  is  1  to  2.  Under  specially 
trying  conditions,  or  sometimes  when  cement  grout  is  being  used, 
a  1  to  1  mixture  may  be  employed.  With  natural  cement,  the  mix- 
tures are  1  to  2  for  ordinary  work  and  1  to  1  where  greater  strength 


42  •  CEMENTING   MATERIALS 

is  needed.  Natural  cement  is  not  used  for  reinforced  concrete  work. 
The  choice  of  ratios  has  usually  been  well  on  the  side  of  safety,  and 
good  results  have  been  obtained  in  practice  by  this  method,  although 
equally  good  work  at  less  cost  might  in  many  instances  have  been 
obtained  by  more  careful  study  of  the  materials  in  proportioning 
the  ingredients  of  the  mortar. 

In  comparing  the  mortar-making  qualities  of  various  sands, 
it  is  found  that  the  amount  of  cement  necessary  to  make  mortar 
of  the  same  strength  from  different  sands  depends  mainly  upon 
the  fineness  and  density  of  the  sands.  The  office  of  the  cement 
paste  in  mortar  is  to  coat  the  grains  of  sand  and  fill  the  voids  between 
them.  In  fine  sand  the  surface  to  be  coated  with  cement  is  greater 
than  in  coarse  sand.  Dense  sand,  with  grains  of  varying  sizes, 
presents  less  voids  to  be  filled  than  more  uniform  sand. 

It  is  desirable  that  careful  study  be  given  to  the  sands  to  be  used 
in  any  important  work  before  finally  deciding  upon  the  proportions 
of  the  materials,  and  that  final  judgment  be  based  upon  actual  tests 
of  the  mortar  itself. 

Frequently  a  mixture  of  a  fine  with  a  coarse  sand,  or  of  crusher 
dust  with  sand  may  be  so  proportioned  as  to  give  economical  results 
in  the  saving  of  cement,  while  at  the  same  time  improving  the  mortar. 

33.  Mixing  Mortar. — In  mixing  mortar  by  hand  a  water-tight 
box  or  platform  is  used.  The  required  quantity  of  sand  is  spread 
over  the  floor  of  the  box  and  the  cement  distributed  evenly  over 
the  sand.  The  cement  and  sand  are  then  mixed  together  with  a 
hoe  or  shovel  until  the  cement  is  uniformly  distributed  through 
the  sand,  as  shown  by  the  even  color  of  the  mixture  diy.  It  is 
important  that  the  dry  materials  be  very  thoroughly  mixed  before 
water  is  added.  A  uniform  mixture  will  not  otherwise  be  obtained. 
When  the  mixing  of  dry  materials  is  complete,  water  is  added  and 
the  mass  worked  into  a  stiff  paste.  The  quality  of  the  mortar 
is  materially  affected  by  the  vigor  with  which  it  is  worked  in  bring- 
ing it  to  the  proper  consistency.  After  the  water  has  been  absorbed 
by  the  cement,  vigorous  working  will  make  the  mass  more  plastic, 
and  working  should  continue  until  a  permanent  condition  is  reached. 

Quantity  of  Water. — The  quantity  of  water  to  be  used  in  mixing 
mortar  can  be  determined  only  by  experiment  in  each  instance — 
it  depending  upon  the  nature  of  the  cement  and  sand,  and  the  pro- 
portion of  cement  to  sand.  The  quantity  of  water  used  should  be 
the  least  consistent  with  reducing  the  mortar  to  the  required  condi- 
tion of  plasticity  by  vigorous  working.  Additional  water  should 
not  be  used  to  save  labor  in  working. 


CEMENT   MORTAR  43 

Mixing  should  be  quickly  and  energetically  done,  only  such 
quantity  being  mixed  at  once  as  can  be  used  before  initial  set  takes 
place.  A  considerable  quantity  is  sometimes  mixed  dry  and  left 
to  stand  until  needed  before  adding  water.  If  this  is  done  with 
damp  sand,  the  cement  may  be  acted  upon  by  the  moisture  in  the 
sand  to  the  injury  of  the  mortar.  Quick-setting  cements  are  par- 
ticularly liable  to  injury  from  this  cause. 

Retempering. — Masons  frequently  mix  mortar  in  considerable 
quantities,  and  if  the  mass  becomes  stiffened  before  being  used, 
add  more  water  and  work  again  to  plastic  condition.  After  the 
second  tempering  the  cement  is  much  less  active  than  at  first,  and 
remains  a  longer  time  in  a  workable  condition.  This  practice  is 
not  approved  by  engineers  and  is  not  permitted  in  good  engineering 
construction,  although  there  is  some  dispute  as  to  the  extent  of  the 
injurious  effects. 

Cement  when  retempered  becomes  very  slow  in  action,  both 
in  setting  and  hardening.  The  quicker-setting  cements  are  usually 
more  affected  than  the  slow  setting.  The  strength  during  the  earlier 
periods  of  hardening  is  lessened,  although  the  final  strength  may 
not  be  impaired.  Portland  cement  may  ordinarily  be  used  for 
two,  or  sometimes  three  hours  after  mixing  without  appreciably 
affecting  its  action.  When  retempered  after  a  longer  period  it  will 
usually  become  slower  in  action,  but  may  in  some  cases  gain  as 
much  strength  in  thirty  to  sixty  days. 

Continuous  working  materially  improves  the  strength  of  mortar, 
and  when  allowed  to  stand  after  mixing  it  should  be  frequently 
worked. 

Grout. — Mortar  when  made  thin,  so  that  it  can  be  poured  into 
cracks  or  small  openings,  is  known  as  grout.  Mixtures  of  cement 
and  sand  used  in  this  manner  are  difficult  to  handle  without  sepa- 
ration of  the  materials.  They  should  be  used  only  under  excep- 
tional circumstances  and  when  stiffer  mortar  cannot  be  applied. 

34.  Yield  of  Mortar.— The  volume  of  mortar  formed  by  mixing 
given  quantities  of  cement  and  sand  depends  mainly  upon  the  den- 
sities of  the  materials.  It  is  affected  by  the  method  of  preparing 
the  mortar,  the  uniformity  of  the  mixture,  and  the  degree  of  com- 
pactness. The  net  volume  of  materials  entering  into  the  com- 
position of  mortar  is  readily  found  from  their  weights  and  densities, 
but  it  represents  only  approximately  the  resulting  volume.  An 
accurate  knowledge  of  the  yield  of  any  particular  mixture  is  to  be 
obtained  only  by  experimenting  upon  the  materials  to  be  employed. 

The  amount  of  cement  paste  made  by  a  given  weight  of  cement 


44 


CEMENTING   MATERIALS 


powder  varies  with  the  specific  gravity  of  the  cement  and  the  amount 
of  water  necessary  in  gaging.  The  lighter  cements  require  more 
water  and  yield  less  paste  for  a  given  volume  of  cement  than  the 
heavier  ones.  To  form  a  cubic  foot  of  plastic  paste  requires  usually 
from  80  to  95  pounds  of  natural  cement,  while  from  95  to  101  pounds 
of  Portland  cement  are  necessary. 

Table  IV  gives  approximate  quantities  of  materials  ordinarily 
required  for  1  cubic. yard  of  compact  plastic  mortar.  A  barrel  of 
cement  is  taken  as  4  cubic  feet,  corresponding  to  a  weight  of  94 
pounds  per  cubic  foot  for  Portland  cement  and  70  pounds  for  natural 
cement.  The  sand  is  dry  and  measured  loose. 

TABLE  IV.— MATERIALS  FOR   1   CUBIC  YARD  OF   MORTAR 


PROPORTIONS. 

QUANTITY  OF  SAND  TO  1 
SACK  CEMENT. 

MATERIALS  FOR  1  Cu.  YD.  COMPACT, 
PLASTIC  MORTAR. 

Cement. 

Sand. 

Portland, 
Cu.  Ft. 

Natural, 
Cu.  Ft. 

Cement,  Barrels. 

Sand,  Cu.  Yds. 

1 

0 

6.75  to  7.  85 

1 

1 

1.0 

1.3 

4.25  to  4.  75 

0.63  to  0.70 

1 

2 

2.0 

2.7 

2.95  to  3.  15 

0.87  to  0.93 

1 

3 

3.0 

4.0 

2.  20  to  2.  37 

0.98  to  1.04 

1 

4 

4.0 

5.3 

1.75  to  1.85 

1.03  to  1.09 

The  differences  in  quantities  are  mainly  due  to  variations  in 
the  fineness  of  the  sand,  in  the  amount  of  moisture  contained  by  the 
sand,  and  in  the  compactness  given  to  the  mortar.  Less  materials 
are  required  when  using  fine  than  when  using  coarse  sand;  more 
materials  are  required  when  the  sand  is  moist  than  when  it  is  dry. 
The  compactness  of  the  mortar  is  affected  by  the  quantity  of  water 
used  in  mixing  and  the  method  of  placing  the  mortar. 

35.  Mixtures  of  Lime  and  Cement. — The  addition  of  slaked  or 
hydrated  lime  to  cement  mortar  causes  the  mortar  to  work  more 
smoothly,  and  makes  it  easier  and  more  economical  to  handle  in 
masonry  construction. 

A  lean  cement  mortar  may  be  improved  in  density  and  strength 
by  the  addition  of  a  small  quantity  of  lime  paste.  Lime  in  larger 
quantities,  or  lime  added  to  rich  mortar,  diminishes  the  strength 
of  the  mortar  but  may  sometimes  be  economical,  through  cheapen- 
ing the  mortar  and  improving  its  working  qualities,  when  high 
strength  is  not  of  special  importance. 

Lime  may  be  used  with  cement  either  by  mixing  lime  paste  with 


CEMENT  MORTAR  45 

cement  mortar,  or  by  mixing  dry  hydrated  lime  with  cement  before 
mixing  the  mortar.  Lime  must  always  be  thoroughly  slaked  before 
mixing  with  cement,  as  unhydrated  lime  in  cement  mortar  is  always 
a  detriment.  It  is  also  essential  that  the  mixture  be  very  uniform, 
and  that  the  mortar  be  worked  to  an  even  color.  For  this  reason, 
the  use  of  dry  hydrated  lime  is  to  be  preferred  over  lime  paste. 

In  proportioning  lime  to  cement,  the  method  of  measurement 
is  important.  Hydrated  lime  from  nearly  pure  limestone  contains 
about  75  per  cent  of  quicklime  and  ordinary  lime  paste  contains 
about  40  per  cent  of  lime  by  weight.  About  25  pounds  of  quick- 
lime are  required  to  make  a  cubic  foot  of  lime  paste. 

Experiments  upon  mixtures  of  lime  and  cement  show  that  10 
to  15  per  cent  of  lime  (measured  as  unslaked  lime)  may  be  substi- 
tuted for  an  equal  weight  of  cement  in  a  1  to  3  cement  mortar  with- 
out sensibly  decreasing  the  strength  of  the  mortar.  In  some  instances 
when  not  more  than  10  per  cent  of  lime  is  used  the  strength  is 
increased  and  the  mortar  made  more  dense.  As  the  proportion 
of  lime  is  increased  the  strength  of  the  mortar  is  lessened.  For 
mortars  leaner  than  1  to  3  of  Portland  cement  the  use  of  a  small 
amount  of  lime  is  usually  an  advantage. 

With  some  natural  cements,  lime  may  be  used  to  replace  cement 
to  the  extent  of  25  to  30  per  cent  of  the  weight  of  the  cement  with- 
out appreciable  loss  of  strength  in  the  mortar.  Cement  so  treated 
becomes  slower  in  action  and  is  longer  in  gaining  strength  than  when 
used  without  lime.  Mixtures  of  this  kind  with  either  Portland  or 
natural  cement  are  frequently  used  in  mortar  for  ordinary  building 
operations.  Hydrated  lime  is  sometimes  added  to  cement  for  the 
purpose  of  rendering  the  mortar  less  permeable  where  water-tight 
work  is  needed,  and  is  also  sometimes  added  to  Portland  cement 
concrete  in  small  quantity  to  make  the  concrete  flow  more  readily 
in  filling  the  forms. 

36.  Strength  of  Cement  Mortar. — The  strength  of  cement  mortar 
is  dependent  upon  the  quality  and  proportions  of  cement  and  sand; 
the  quantity  of  water  used  in  gaging;  the  method  of  mixing  and 
thoroughness  of  working;  the  temperature  and  moisture  conditions 
under  which  it  is  kept  during  hardening;  the  age  of  the  mortar. 

The  effect  upon  tensile  strength  of  varying  proportions  of  cement 
and  sand  is  shown  in  Fig.  2,  which  gives  the  relative  strengths  for 
an  average  Portland  cement,  or  cement  paste,  and  mortars  with 
standard  sand,  for  a  period  of  one  year  after  mixing.  Individual 
cements  may  vary  quite  widely  from  the  curves  shown.  Some 
gain  strength  more  slowly  at  first  and  continue  to  gain  for  a  longer 


46 


CEMENTING  MATERIALS 


period.     Others  have  greater  early  strength  and   show  more  loss 
of  strength  during  the  period  of  retrogression. 

Nearly  all  Portland  cements  after  gaining  strength  rapidly  for 
a  time  reach  a  maximum  and  then  lose  strength  for  a  period.  This 
loss  of  strength  is  usually  regained  later.  It  seldom  occurs  in  less 
than  three  months  or  more  than  one  year  after  the  mortar  is  mixed. 
Cement  which  gains  strength  very  rapidly  and  has  high  early 
strength  is  apt  to  suffer  greater  loss  of  strength  later  than  cements 


1000 


I         a       3       A-       5       <o       7        6       3       10      II       12 
TIME-MONTHS 

FIG.  2. — Strength  of  Portland  Cement  Mortar. 

of  more  moderate  action,  and  less  likely  to  regain  fully  the  losses. 
Mortars  usually  show  less  of  the  effects  of  retrogression  than  cement 
paste,  and  frequently  continue  to  gain  strength  for  much  longer 
periods. 

Fig.  3  shows  average  values  for  good  grades  of  natural  cement. 
These  cements  vary  more  widely  than  Portlands.  They  gain 
strength  much  more  slowly  arid  continue  to  gain  for  a  longer  period. 

Character  of  Sand. — Coarse,  well-graded  sand  usually  gives 
higher  strength -in  cement  mortar  than  standard  Ottawa  sand  while 
fine  or  poorly  graded  sand  may  fall  below  the  strength  shown  by 
standard  sand.  Sands  showing  less  than  75  per  cent  of  the  strength 


CEMENT   MORTAR 


47 


given  by  standard  sand  are  poor  materials  and  are  sometimes  rejected 
by  specifications  for  masonry  materials. 

Fineness  of  Cement. — The  fineness  of  the  cement  has  an  important 
influence  upon  the  strength  of  mortar.     Table  V  shows  the  results 


500 


345675$ 

TIME  -   MONTHS 

FIG.  3. — Strength  of  Natural  Cement  Mortars. 


to    ii 


of  a  series  of  tests  made  upon  Portland  cement  by  Mr.  Richard  K. 
Meade.1  In  making  these  tests  a  bag  of  cement  was  selected  and 
divided  into  five  parts,  and  each  of  these  ground  to  a  different  degree 
of  fineness. 


TABLE  V.— STRENGTH    OF    THE    SAME    CEMENT    GROUND    TO 
VARIOUS  DEGREES  OF  FINENESS 

Tensile  strength  in  pound  per  square  inch. 


Age,  Days. 

Neat  or  Sand. 

PER  CENT  PASSING  No.  200  SIEVE. 

80 

85 

90 

95 

100 

1 

Neat 

396 

241 

308 

282 

200 

7 

Neat 

955 

796 

749 

627 

558 

28 

Neat 

963 

840 

775 

626 

594 

1 

1  to  3  sand 

235 

248 

351 

363 

382 

28 

1  to  3  sand 

297 

353 

468 

498 

576 

7 

1  to  4  sand 

160 

204 

234 

247 

263 

28 

1  to  4  sand 

224 

266 

324 

377 

392 

The  strength  of  neat  cement  is  decreased  by  fine  grinding,  while 

the  strength  of  sand  mortar  is  increased  by  find  grinding.     The 

same  strength  may  be  reached  in  sand  mortar  by  using  less  cement 

when  the  cement  is  finely  ground  than  when  it  is  coarsely  ground. 

1  Proceedings  American  Society  for  Testing  Materials,  1908,  p.  412. 


48  CEMENTING   MATERIALS 

In  the  table  it  is  shown  that  the  strength  of  1  to  4  mortar  with 
cement  90  per  cent  fine  is  stronger  than'  1  to  3  mortar  with  cement 
80  per  cent  fine. 

The  desirability  of  fine  grinding  depends  upon  the  relative  costs 
of  cement  ground  to  different  degrees  of  fineness.  Fine  grinding 
increases  the  rapidity  of  setting  very  rapidly,  and  many  Portland 
cements  if  ground  so  that  95  per  cent  passes  the  No.  200  sieve  become 
so  quick  setting  that  they  could  not  be  used  for  ordinary  work. 
In  order  to  secure  greater  fineness,  the  methods  of  manufacture 
would  need  considerable  modification. 

Effect  of  Consistency  upon  Strength. — The  amount  of  water  used 
in  mixing  mortar  necessarily  depends  upon  the  requirements  of  the 
use  to  be  made  of  the  mortar.  The  mortar  used  in  concrete  is 
usually  much  softer  than  that  employed  in  masonry  construction, 
or  than  the  consistency  used  in  testing. 

For  well-compacted  mortar,  strength  decreases  as  the  quantity 
of  water  used  in  mixing  increases.  The  extent  of  this  effect  varies 
with  the  character  of  the  sand,  being  less  for  coarse  than  for  fine 
sand.  This  difference  is  very  considerable  in  short  time  tests,  but 
disappears  to  considerable  extent  as  the  age  of  the  mortar  increases. 
When  tested  after  seven  and  twenty-eight  days,  mortar  of  standard 
consistency  may  have  nearly  double  the  strength  of  that  mixed  with 
50  per  cent  more  water. 

Cement  mortar  hardens  more  rapidly  and  attains  greater  strength 
if  kept  moist  during  setting  and  the  first  period  of  hardening  than 
if  it  be  exposed  at  that  time  to  dry  air, 

ART.   9.     GYPSUM   PLASTERS 

37.  Classification. — Pure  gypsum  is  a  hydrous  lime  sulphate 
(CaSO4-f2H20).  It  occurs  in  nature  as  a  massive  rock,  or  some- 
times as  gypsum  sand  or  earth.  Native  gypsum  usually  contains 
small  amounts  of  silica,  alumina,  iron  oxide,  and  calcium  carbonate. 
Alabaster  is  a  massive  rock  of  nearly  pure  white  gypsum. 

Native  gypsum  is  ground  and  used  as  a  dressing  for  certain  soils. 
It  is  also  used  quite  extensively  as  an  adulterant  in  the  manufacture 
of  Portland  cement.  (See  Section  12.) 

Gypsum  plasters  are  made  by  calcining  gypsum  sufficiently  to 
drive  off  part  or  all  of  the  water  of  combination.  When  this  dehydra- 
tion is  accomplished  at  a  temperature  below  190°  C.,  three-fourths 
of  the  water  is  driven  off  and  the  resultant  product  is  called  plaster 
of  paris  (CaSO4+iH2O).  At  a  temperature  above  190°  C.  all  of 


GYPSUM  PLASTERS  49 

the  water  is  driven  off  and  the  product  is  known  as  flooring  plaster 
(CaSO4).  These  products  are  modified  by  adding  certain  substances 
to  the  gypsum  before  calcining,  or  by  the  use  of  impure  gypsum. 

The  following  classification  of  gypsum  plasters  is  given  by 
E.  C.  Eckel  in  his  "  Cements,  Limes  and  Plasters  ": 

CLASSIFICATION  OF  PLASTERS 

(a)  Produced  by  the  incomplete  dehydration  of  gypsum,  the  calcination 
being  carried  on  at  a  temperature  not  exceeding  190°  C. 

(1)  Plaster  of  paris,  produced  by  the  calcination  of  a  pure  gypsum,  no 
foreign  materials  being  added  either  during  or  after  calcination. 

(2)  Cement  plaster  (often  called  patent  or  hard  wall  plaster)  produced  by 
the  calcination  of  a  gypsum  containing  certain  natural  impurities, 
or  by  the  addition  to  a  calcined  pure  gypsum  of  certain  materials 
which  serve  to  retard  the  set  or  render  more  plastic  the  product. 

(&)  Produced  by  the  complete  dehydration  of  gypsum,  the  calcination  being 
carried  on  at  ternperatures  exceeding  190°  C. 

(3)  Flooring  plaster,  produced  by  the  calcination  of  a  pure  gypsum. 

(4)  Hard  finish  plaster,  produced  by  the  calcination  at  a  red  heat  or  over, 
of  gypsum  to  which  certain  substances  (usually  alum  or  borax)  have 
been  added, 

Plaster  of  paris  and  cement  plaster  are  usually  burned  at  tem- 
peratures from  140°  to  180°  C.,  the  difference  between  them  being 
due  to  the  substances  added  to  the  gypsum  in  making  the  cement 
plaster.  Flooring  plaster  and  hard-finish  plaster  are  burned  at 
400°  to  500°  C.  for  three  or  four  hours.  If  the  heat  be  too  high  or 
too  prolonged,  the  plaster  may  be  injured,  becoming  very  slow  in 
action,  and  is  called  dead-burnt  plaster. 

Keene's  Cement  is  a  well-known  hard-finish  plaster  made  by  the 
double  calcination  of  gypsum,  alum  being  added  between  the  two 
heatings. 

Cement  plaster,  after  being  calcined,  requires  the  addition  of 
some  material  as  a  retarder  to  decrease  the  rapidity  of  set.  This 
is  usually  a  very  small  quantity  (0.1  to  0.2  per  cent)  of  organic 
matter  such  as  blood  or  glue.  Hydrated  lime  or  clay  is  usually 
added  to  gypsum  wall  plasters  to  increase  their  plasticity  and  make 
them  work  better.  With  plasters  made  from  gypsum  earth  contain- 
ing clay  this  is  unnecessary. 

38.  Properties  and  Uses. — Gypsum  plasters  when  mixed  with 
water  set  and  harden  through  the  combination  of  the  water  with 
the  plaster  to  again  form  gypsum.  The  setting  of  plaster  of  paris 
is  rapid,  requiring  from  about  five  to  fifteen  minutes.  Cement 


50  CEMENTING   MATERIALS 

plaster  sets  more  slowly,  requiring  from  one  to  three  hours.  Floor 
plaster  and  hard-finish  plaster  are  slow  setting, 

Very  few  data  are  available  concerning  the  strength  of  gypsum 
plasters,  which  usually  gain  strength  rapidly  for  a  few  days,  reach- 
ing a  maximum  in  three  or  four  weeks,  and  then  suffer  retrogression 
in  strength  for  a  time.  A  series  of  tests  made  by  Professor  Marston 
of  Iowa  State  College  on  hard  wall  plasters  indicate  a  strength  for 
neat  plaster  of  300  to  500  lbs./in.2  one  month  after  mixing.  About 
80  per  cent  as  much  for  1  to  1  mortar  and  50  per  cent  as  much  for 
1  to  2  mortar  with  sand.  These  strengths  would  not  be  reached 
under  the  conditions  of  ordinary  use.  The  strength  is  much  less 
when  the  mortar  is  kept  damp  during  the  period  of  hardening. 

Plaster  of  paris  sets  too  rapidly  for  use  in  construction,  although 
it  is  used  to  some  extent  combined  with  other  materials,  as  in  hard 
finish,  composed  of  plaster  of  paris,  lime  putty,  and  marble  dust. 
It  is  commonly  employed  for  casting  plaster,  where  quick  set  is 
desired. 

Cement  and  hard  wall  plasters  are  used  for  making  various  wall 
plasters,  being  usually  mixed  with  hair,  asbestos,  or  wood  fiber,  and 
clay  or  hydrated  lime.  They  are  received  upon  the  work  ready  for 
use  and  do  not  require  the  time  or  space  for  preparation  needed  for 
lime  plaster,  but  are  not  so  plastic  and  smooth  to  work. 

Hard-finish  plasters  are  used  in  a  number  of  ways  in  making 
solid  or  hollow  blocks  and  tiles  for  use  in  construction  of  partitions 
and  in  finishing  floors  and  ceilings.  Mixed  with  sawdust,  blocks 
are  formed  which  may  be  nailed  into  place.  Blocks  reinforced  with 
steel  are  now  being  made  for  use  in  supporting  roofs.  (See  Art.  18.) 


CHAPTER  III 

STONE  MASONRY 

ART.   10.     BUILDING   STONE 

39.  Qualities  for  Building  Stone. — The  choice  of  stone  for  use 
in  important  structures  is  always  a  matter  of  moment,  and  frequently 
involves  considerable  difficulty,  on  account  of  the  wide  variation 
in  the  characteristics  of  the  stones  commonly  used.  Stones  belong- 
ing to  the  same  classes  frequently  differ  greatly  in  their  physical 
properties  and  much  care  needs  to  be  exercised  in  securing  materials 
of  proper  strength  and  endurance. 

The  qualities  which  are  of  importance  in  the  selection  of  stone 
for  structural  uses  are  strength,  durability,  appearance,  and  cost. 
The  relative  importance  of  these  in  any  particular  structure  depends 
upon  the  location  of  the  structure  and  the  purpose  for  which  it  is 
intended.  For  ordinary  masonry,  the  most  important  quality  of 
the  stone  is  usually  its  durability.  The  element  of  strength  is 
commonly  of  minor  consequence,  except  in  portions  of  a  structure 
where  the  conditions  are  such  as  to  bring  severe  stresses  upon  the 
masonry.  A  pleasing  appearance  is  always  desirable,  but  any  stone 
possessing  proper  structural  qualities  may  usually  be  so  employed 
as  to  produce  a  good  effect,  where  the  purpose  of  the  structure  is 
not  distinctly  artistic.  In  architectural  and  monumental  work, 
the  appearance  of  the  stone  may  be  of  first  importance,  while  the 
strength  of  the  stone,  or  its  cost,  is  of  less  consequence.  Stone  for 
such  uses,  when  in  exposed  situations,  must  possess  durability  in 
order  to  preserve  the  beauty  of  the  structure  and  prevent  disfigure- 
ment or  discoloration  of  its  surfaces. 

The  cost  of  the  stone  is  always  a  matter  of  importance,  commonly 
limiting  the  choice,  and  frequently  being  the  determining  factor  in 
selection  of  stone.  The  cost  of  stone  depends  mainly  upon  the 
ease  with  which  it  may  be  quarried  and  worked,  and  the  distance 
and  means  of  transportation  to  the  place  where  it  is  to  be  used. 
The  equipment  of  a  quarry  for  handling  and  working  stone  often 
determines  its  availability  for  a  particular  use.  The  kind  of  finish 

51 


52  STONE  MASONRY 

to  be  given  the  surfaces,  and  the  suitability  of  the  material  to  the 
proposed  treatment  are  also  important  in  their  effects  upon  cost. 

A  good  building  stone  should  be  dense  and  uniform  in  structure, 
and  should  have  no  seams  or  crow-foots  filled  with  material  which 
may  disintegrate  and  form  cracks  upon  exposure.  The  fracture 
should  be  clean  and  sharp,  and  the  surface  free  from  earthy  appear- 
ance. 

Hardness  and  toughness  are  important  properties  in  a  stone 
which  is  to  be  subjected  to  wear  or  abrasion  of  any  kind.  Stones 
lacking  in  toughness  and  easily  abraded  have  sometimes  been  seri- 
ously defaced  by  dust  and  sand  particles  carried  by  strong  winds. 
The  hardness  of  the  stone  depends  both  upon  the  hardness  of  the 
minerals  of  which  it  is  composed  and  upon  the  firmness  with  which 
they  are  bound  together.  Toughness  depends  upon  the  resistance 
to  separation  of  the  mineral  grains.  Rocks  of  hard  material  may 
be  lacking  in  toughness  and  easily  worked  when  weakly  cemented. 

40.  Classification  of  Building  Stones. — All  rocks  are  aggregations 
of  various  mineral  constituents,  more  or  less  firmly  held  together. 
Geologically,  as  to  their  mode  of  occurrence,  they  are  divided  into 
three  groups,  as  follows: 

(1)  Igneous  Rocks. — Those  which  have  been  forced  up  in  a  molten 
condition  from  unknown  depths  and  subsequently  cooled.     When 
the  molten  rock  has  cooled  and  solidified  below  the  surface  of  the 
ground  it  is  known  as  plutonic,  when  above  ground  as  volcanic. 

(2)  Sedimentary  or  Stratified   Rocks. — Rocks   formed   by  being 
deposited  as  sediment  in  layers,  and  consequently  showing  bedding 
lines  and  stratifications.     Limestones  and  sandstones  belong  in  this 
class. 

(3)  Metamorphic  Rocks,  formed  by  subjecting  igneous  or  strati- 
fied rocks  to  great  heat  or  pressure  or  to  both. 

Building  stones  may  also  be  classified  according  to  their  chemical 
and  physical  properties  into  three  groups: 

Crystalline,  siliceous  rocks,  including  granites,  gneisses,  traps,  etc. 

Calcareous  rocks,  including  limestones  and  marbles. 

Fragmental  rocks,  including  sandstones  and  slates. 

Granite  is  a  crystalline  siliceous  rock  of  igneous  origin.  It  con- 
sists essentially  of  quartz,  with  some  feldspar  and  usually  mica. 
It  is  readily  quarried  into  blocks  of  regular  shape,  but  is  very  hard 
and  tough  and  is  expensive  to  cut  for  ornamental  work.  It  is  the 
strongest  and  most  durable  of  our  building  stones  in  common  use, 
and  is  very,  generally  employed  in  important  work  where  these 
qualities  are  of  special  importance.  Heavy  foundations,  base  courses, 


BUILDING  STONE  53 

water  tables,  and  columns  in  important  buildings  are  very  commonly 
of  granite. 

The  color  of  granite  is  usually  gray,  but  pink,  red,  and  black 
granites  are  found.  It  is  largely  used  in  monumental  work  and  in 
architecture  for  exterior  work  where  the  most  beautiful  and  durable 
results  are  desired.  The  use  of  machinery  for  working  the  stone 
has  made  this  use  economically  feasible. 

Syenite  is  a  rock  similar  to  granite,  but  composed  mainly  of  feld- 
spar instead  of  quartz.  It  has  much  the  same  qualities  as  granite 
and  is  usually  classed  as  granite  when  used. 

Diorite  and  Gabbro  are  rock  of  the  same  general  character  as 
granite  but  differing  in  mineral  composition.  They  are  usually 
classed  commercially  as  granites. 

Gneiss  is  a  metamorphic  rock  of  the  same  composition  as  granite. 
It  is  metamorphosed  granite  or  syenite,  and  usually  classed  as  granite, 
being  often  called  stratified  or  bastard  granite.  Gneiss  differs  from 
granite  in  having  a  somewhat  laminated  structure  which  causes  it 
to  split  in  parallel  layers.  It  is  often  used  for  flagging  and  paving 
blocks  on  this  account. 

Granites  are  found  quite  widely  distributed  in  the  mountain 
regions  of  the  United  States.  The  main  supply  comes  from  the  New 
England  States,  where  large  quarries  are  in  operation  and  have 
gained  wide  reputation.  Commercial  granites  of  good  quality  are 
found  in  the  South  Atlantic  States,  in  Wisconsin  and  Missouri, 
while  Montana,  Wyoming,  Colorado,  California,  and  Washington 
are  plentifully  supplied  with  granite  which  is  comparatively  unde- 
veloped. 

Limestones  are  sedimentary  calcareous  rocks,  consisting  mainly 
of  the  mineral  calcite,  which  is  composed  of  calcium  carbonate 
(CaCOs).  They  also  usually  contain  small  amounts  of  iron  oxide, 
silica,  and  clay.  Magnesia  is  also  commonly  present  in  the  pure 
limestones  in  very  small  amounts,  and  varying — through  the  mag- 
nesian  limestones,  in  which  10  per  cent  or  more  of  magnesia  is  pres- 
ent— to  dolomite,  which  consists  mainly  of  the  mineral  dolomite 
(CaMg)C03. 

Limestone  varies  from  stone  soft  enough  to  cut  with  a  saw  to 
hard  material  which  works  with  difficulty.  Some  of  the  soft  stones 
harden  on  exposure  and  are  durable  in  use,  the  Topeka  stone  used 
in  Kansas  being  of  this  character.  Many  of  the  fine-grained,  light- 
colored  limestones  form  excellent  building  material;  they  are  hard 
and  tough  and  show  good  durability  in  use,  although  inferior  in  this 
respect  to  the  best  sandstone  and  granite.  Some  of  them  are  used 


54 


STONE   MASONRY 


in  ornamental  work  and  take  good  polish.  Stone  containing  pyrite 
is  apt  to  show  poor  weathering  qualities,  while  spots  of  flint  found 
in  many  of  these  stones  are  objectionable  on  account  of  weathering 
unevenly  and  sometimes  causing  the  stone  to  split  under  frost  action. 
The  following  analysis  of  typical  limestones  are  given  by  Ries  l 
to  show  the  range  of  chemical  composition : 


I 

II 

III 

IV 

Calcium  carbonate  (CaCOs)  
Magnesian  carbonate  (MgCO3).. 
Alumina  (A^Os)  1 

97.26 
0.37 

54.53 
39.41 

81.43 
15.04 

98.91 
0.58 

Ferric  oxide  (FejOa)  J 
Silica  (SiO2  .  . 

0.49 
1  69 

0.26 
3  96 

0.57 

2  89 

0.63 
0  10 

Water  (H2O) 

1  50 

0  08 

Limestones  exist  in  large  quantities  through  the  States  of  the 
Middle  West,  and  are  locally  developed  in  many  places.  The 
well-known  Bedford,  Indiana,  stone  is  extensively  used  and  shipped 
for  considerable  distances. 

Marbles  are  limestones  which  have  been  subjected  to  metamorphic 
action.  In  composition  they  are  identical  with  limestones,  or  dolo- 
mites, but  are  crystalline  in  texture  and  may  be  polished.  The 
term  marble  is  commonly  used  to  designate  any  limestone  capable 
of  taking  a  polish. 

Marbles  are  commonly  employed  for  interior  finish  in  buildings 
and  for  monumental  work.  The  scarcity  and  cost  of  the  best  marbles 
have  prevented  their  extensive  use  for  ordinary  building  construc- 
tion. Their  weathering  properties  are  similar  to  those  of  limestone, 
although  some  of  the  more  ornamental  ones  are  suitable  for  interior 
work  only.  For  structural  work  the  more  dense  fine-grained  stone 
is  to  be  preferred. 

Sandstones  are  essentially  grains  of  quartz  cemented  together. 
Iron  oxide,  silica,  carbonate  of  lime,  or  clay  may  be  the  cementing 
medium.  The  character  of  the  stone  varies  with  that  of  the  cement 
binding  the  sand  grains. 

Sometimes  other  minerals  than  quartz  are  present  in  sandstones, 
as  feldspar,  mica,  or  pyrite,  thus  modifying  the  character  of  the  stone, 
usually  rendering  it  less  durable.  Sandstones  in  which  silica  is  the 
cementing  material  are  usually  the  most  durable.  They  are  com- 
monly light  in  color.  When  considerable  silica  is  present,  the  stone 

1  BuHding  Stones  and  Clay  Products,  New  York,  1912. 


BUILDING  STONE  55 

is  very  hard  and  difficult  to  work,  while  some  stones  containing  less 
cement  work  easily  and  remain  gritty  under  wear. 

Sandstone  in  which  the  cement  is  iron  oxide  is  usually  of  a  red 
or  brown  color.  These  stones  usually  work  easily,  and  are  often 
durable  in  use  as  building  stones.  When  the  cementing  material 
is  carbonate  of  lime,  the  stone  usually  possesses  fair  strength,  but 
is  not  often  so  durable  as  that  with  silica  or  iron  oxide.  These  stones 
are  usually  light  colored,  soft  and  easy  to  work.  Clay  as  a  cement 
in  sandstone  is  usually  less  desirable  than  the  others;  the  stone 
containing  it  is  not  so  strong;  it  absorbs  water  and  may  be  liable 
to  injury  from  frost.  When  present  in  small  amount  and  uniformly 
distributed  through  the  stone,  clay  may  make  the  stone  easier  to 
work  without  otherwise  injuring  it. 

"  Sandstones,  as  a  rule,  show  good  durability.  Some  of  the 
softer  ones  may  disintegrate  under  frost  action.  Those  with  clay 
seams  are  liable  to  split  with  continued  freezing.  Mica  scales,  if 
abundant  along  the  bedding  planes,  are  also  likely  to  cause  trouble, 
and  this  is  aggravated  if  the  stone  is  set  on  edge  instead  of  on  bed.  A 
striking  example  of  this  is  the  Connecticut  brown  stone  so  extensively 
used  in  former  years  for  fronts  in  many  of  the  Eastern  cities.  In 
order  to  get  a  smooth  surface  it  was  rubbed  parallel  with  the  bedding, 
and  the  stone  set  in  the  building  on  edge.  The  result  is  that  hundreds 
of  buildings  put  up  more  than  fifteen  or  twenty  years  ago  are  scaling 
badly,  and  in  many  cases  the  entire  front  has  been  redressed."  1 

Sandstones  are  of  sedimentary  origin  and  are  more  or  less  in 
layers.  They  should  always  be  laid  on  their  natural  beds,  and  are  apt 
to  scale  off  if  placed  on  edge.  They  vary  in  texture  from  grains  of 
powdery  fineness  to  those  in  which  the  grains  are  of  course  sand. 
The  fine-grained  stones  are  usually  the  strongest  and  most  durable. 

Sandstone  is  quite  widely  distributed  over  the  United  States, 
and  is  one  of  the  most  desirable  and  most  extensively  used  building 
stones.  Many  quarries  are  in  use  throughout  the  country  for  local 
purposes,  while  a  few  quarries  supply  stone  for  wider  distribution. 
The  Berea  stone  of  Ohio  is  frequently  shipped  to  considerable  dis- 
tances. The  Brownstone  of  Connecticut,  Medina  sandstone  of 
western  New  York,  Kettle  River  sandstone  of  Minnesota  are  examples 
of  well-known  stones  in  common  use. 

Slate  is  a  metamorphic  rock  produced  from  clay  or  shale.     It 

is  characterized  by  a  tendency  to  split  into  thin  sheets  with  smooth 

surfaces.     The  direction  of  this  cleavage  is  not  parallel  to  the  bedding 

and  has  probably  been  caused  by  heavy  lateral  pressure.     These 

1  Ries,  Building  Stones  and  Clay  Products,  p.  165. 


56  STONE  MASONRY 

sheets  of  slate  are  strong  under  transverse  loading  and  quite  imper- 
vious to  water.  They  therefore  make  good  roof  covering,  or  may 
be  used  as  flags  for  spanning  openings.  They  are  also  commonly 
used  for  blackboards,  school  slates,  etc.  The  color  of  slate  is  com- 
monly dark  blue,  gray,  or  black,  although  green  and  red  slates  are 
also  common. 

Good  slate  should  be  dense  and  tough  and  not  corrodible  by 
atmospheric  gases.  When  loaded  transversely,  it  should  bend 
appreciably  before  breaking,  and  should  show  a  modulus  of  rupture 
from  7000  to  10000  lbs./in.2 

Most  of  the  slate  now  hi  use  comes  from  the  New  England  and 
Middle  Atlantic  States,  notably  from  Vermont  and  eastern  Pennsyl- 
vania. Important  quarries  have  also  been  opened  in  Arkansas 
and  California. 

41.  Strength  of  Building  Stone. — The  loads  brought  upon 
masonry  structures  are  rarely  sufficient  to  tax  the  strength  of  the 
stone  in  compression.  The'  strength  of  masonry  is  not  directly 
dependent  upon  that  of  the  stone  used  in  its  construction.  The 
strength  of  the  mortar,  thickness  of  joints,  and  the  care  and  accuracy 
used  in  bedding  the  stones  have  important  effects  upon  the  strength 
of  the  masonry.  It  is  desirable  that  building  stone  should  be  strong 
and  capable  of  resisting  heavy  loads,  and  tests  of  the  strength 
of  the  stone  may  show  whether  the  stone  is  of  good  quality  and  fit 
for  use. 

When  stone  is  to  be  used  to  span  openings  and  carry  transverse 
loads,  its  strength  is  important  and  care  should  be  taken  in  its  selec- 
tion. The  ability  of  stone  to  resist  cross-bending  stresses  is  mainly 
dependent  upon  its  tensile  strength.  Tests  of  transverse  strength 
may  serve  to  detect  brittleness  and  lack  of  toughness  or  uniformity 
in  the  texture  of  the  stone. 

Tests  for  Compressive  Strength. — The  compressive  strength  of 
stone  is  determined  by  measuring  the  loads  necessary  to  crush  small 
blocks  cut  from  the  stone.  The  results  of  such  tests  vary  with  the 
sizes  and  shapes  of  the  blocks  tested  and  the  methods  of  placing 
them  in  the  testing  machine.  It  is  necessary  in  comparing  the 
strengths  of  different  stones  to  use  a  standard  form  and  size  of  speci- 
men and  standard  method  of  testing.  It  is  usual  to  use  small  cubes, 
2  inches  on  the  edge.  The  size  does  not  seem  to  very  greatly  affect 
the  resistance  per  unit  area,  but  it  is  desirable  to  use  blocks  of  the 
same  size  in  making  comparative  tests. 

The  shape  of  the  block  is  highly  important  in  its  effect  upon 
the  results  of  such  tests.  When  subjected  to  compression,  materials 


BUILDING  STONE  57 

of  this  kind  break  by  shearing  on  planes  making  angles  of  about 
30°  with  the  direction  of  the  compressing  force.  The  ratio  of  the 
height  of  the  specimen  to  its  lateral  dimensions  is  therefore  important. 
The  strength  of  the  flat  slab  is  much  greater  than  that  of  a  cube, 
while  a  prism  whose  height  is  greater  than  its  breadth  will  show 
less  strength  on  the  test. 

The  test  of  small  specimens  gives  no  indication  of  the  actual 
strength  of  the  stone  in  large  masses,  and  tests  of  this  kind  can  be 
of  value  only  as  indicating  the  quality  of  the  material,  through 
comparison  with  the  results  of  similar  tests  applied  to  other 
stones. 

The  method  of  preparing  the  specimen  may  be  quite  important 
in  the  results  of  a  test.  When  the  dressing  is  done  with  hand  tools, 
the  shocks  frequently  have  the  effect  of  weakening  the  internal 
structure  of  the  stone.  This  effect  with  small  specimens  may  amount 
to  a  decrease  of  30  or  40  per  cent  as  compared  with  the  strength 
of  sawed  blocks.  The  use  of  sawed  test  pieces  is  desirable  in  such 
work. 

The  manner  of  placing  the  specimen  in  the  testing  machine  is 
also  important.  It  is  essential  that  the  test  piece  be  accurately 
centered  in  the  machine,  and  that  it  be  evenly  in  contact  with  the 
pressing  surfaces,  in  order  to  distribute  uniformly  the  compressing 
force  over  the  area  of  the  block.  If  the  surfaces  of  the  test  piece 
be  carefully  ground  to  parallel  planes,  and  the  piece  carefully  centered 
in  the  machine  in  exact  contact  with  the  metal  surfaces,  the  best 
results  will  be  obtained.  This  method,  however,  involves  con- 
siderable labor  in  preparation  of  the  specimen,  and  is  expensive. 
The  more  common  method  is  to  set  the  specimen  in  a  thin  bedding 
of  plaster  of  paris  between  the  plates  of  the  machine  and  leave  it 
under  light  pressure  for  a  few  minutes,  to  allow  the  plaster  of  paris 
to  set,  before  applying  the  load.  This  method,  if  carefully  handled, 
gives  uniform  results,  although  the  strength  shown  is  somewhat 
less  than  that  obtained  by  using  ground  surfaces. 

A  block  of  stone  may  have  much  less  strength  in  one  direction 
than  in  another.  Most  rocks  have  planes  of  cleavage  in  one  direc- 
tion in  which  they  split  more  easily  than  in  other  directions.  These 
planes  are  usually  parallel  to  the  natural  bed  of  the  rock  and  are 
known  as  the  rift  of  the  rock.  Care  should  be  taken  to  place  the 
test  specimen  on  its  natural  bed,  or  in  such  position  that  the  com- 
pression is  applied  in  a  direction  normal  to  the  rift. 

Compressive  Strength. — The  results  of  tests  upon  building  stones 
show  a  wide  variation  in  compressive  strengths  of  different  samples 


58  STONE  MASONRY 

of  the  same  classification,  as  well  as  between  different  classes  of 
stone. 

Hard  limestones  usually  show  crushing  strengths  of  8000  to 
12,000  lbs./in.2,  although  softer  stones  of  good  quality  may  run 
from  3000  to  6000  lb./in.2 

Sandstones  used  in  building  vary  in  compressive  strength  from 
about  4000  to  15,000  lb./in.2  The  better  grades  of  stone  usually 
reach  9000  to  12,000  lb./in.2 

Granites  of  good  quality  should  show  a  crushing  strength  of 
10,000  to  20,000  lb./in.2 

Transverse  Strength. — Tests  of  transverse  strength  are  usually 
made  on  a  small  bar  of  stone,  1  inch  square  in  section,  and  the  method 
of  preparing  the  specimen  is  important  in  its  effect  upon  the  results 
of  the  test.  Comparatively  little  data  exist  concerning  the  strengths 
of  stone  under  transverse  loadings.  The  following  table  gives 
approximate  values  which  have  been  obtained  for  ordinary  stone 
used  in  building. 

MODULUS  OF  RUPTURE,   LB./iN.2 

Granite from  1400  to  2500 

Limestone from    500  to  3000 

Sandstone from    600  to  2000 

In  selecting  stone  for  use  as  lintels,  or  where  it  is  to  carry  trans- 
verse loads,  it  is  desirable  that  the  stone  be  tested  in  blocks  of  size 
comparable  to  those  in  which  it  is  to  be  used.  The  results  of  tests 
upon  small  specimens  is  not  of  much  value  for  this  purpose. 

The  table  on  p.  59,  by  Herbert  F.  Moore,  is  taken  from  Merri- 
man's  "  American  Civil  Engineer's  Pocket  Book." 

42.  Durability  of  Building  Stone. — That  stone  should  be  durable 
under  the  conditions  of  use  is  evidently  one  of  the  most  important 
points  to  be  considered  in  the  selection  of  material  for  use  in  con- 
struction. The  situation  in  which  the  stone  is  to  be  placed  and  the 
climatic  or  other  conditions  which  may  affect  the  durability  should 
therefore  be  carefully  considered.  Local  conditions  have  frequently 
been  overlooked  in  selecting  stone,  with  disastrous  results.  The 
White  House  at  Washington  is  of  sandstone  which  requires  frequent 
painting.  The  obelisk,  in  perfect  condition  after  long  exposure  in 
Egypt,  began  to  disintegrate  almost  immediately  when  set  up  in 
New  York  City.  The  Parliament  House,  built  of  stone  selected 
with  the  greatest  care,  is  not  able  to  resist  the  disintegrating  in- 
fluences of  the  London  atmosphere. 


BUILDING  STONE 


59 


DATA  FOR  BUILDING  STONES  OF  GOOD  QUALITY 
VALUES  BASED  MAINLY  ON  TEST  DATA  FROM  THE  WATERTOWN  ARSENAL 


Kind  of  Stone. 

Weight 
Lbs. 
per 

Com- 
pressive 
Strength, 
Lbs. 

Shearing 
Strength, 
Lbs. 

Modulus 
of 
Rupture, 
Lbs. 

Modulus 
of 
Elasticity, 
Lbs. 

Coefficient 
of 
Expansion 

Absorp- 
tion of 
Water 
Per 

Cubic 
Feet. 

per 
Square 
Inch. 

per 

Square 
Inch. 

per 

Square 
Inch. 

per 
Square 
Inch. 

£ 

Cent 
of 
Weight 

of  Stone. 

Granite, 

160 
to 

15,000 
to 

1800 

to 

1200 
to 

5,900,000 

to 

range,        ^ 

170 

26,000 

2800 

2200 

9,800,000 

Average.  . 

165 

20,200 

2300 

1600 

7,500,000 

0.0000040 

0.5 

Sandstone, 

135 

6,700 

1200 

500 

1,000,000 

'  \ 

to 

to 

to 

to 

to 

range,        [ 

150 

19,000 

2500 

2200 

7,700,000 

Average  .  . 

140 

12,500 

1700 

1500 

3,300,000 

0.0000055 

5.0 

Limestone, 

140 

3,200 

1000 

250 

4,000,000 

'  \ 

to 

to 

to 

to 

to 

range,        [ 

180 

20,000 

2200 

2700 

14,000,000 

Average  .  . 

160 

9,000 

1400 

1200 

8,400,000 

0.0000045 

7.7 

Marble,        j 

160 
to 

10,300 
to 

1000 
to 

850 
to 

4,000,000 
to 

range,       | 

180 

16,100 

1600 

2300 

12,600,000 

Average.  . 

170 

12,600 

1300 

1500 

8,200,000 

0.0000045 

0.4 

( 

170 

140,000 

7000 

13,900,000 

Slate, 

to 

to 

to 

to 

range,       j 

180 

30,000 



11,000 

16,200,000 

Average.  . 

175 

150,000 

8,500 

14,000,000 

0.0000058 

0  5 

Trap,  average 

185 

20,000 

V«10 

The  range  of  changes  in  temperature,  presence  of  moisture  and 
gases  in  the  atmosphere,  and  the  action  of  winds  and  dust  are  the 
principal  causes  of  deterioration  in  stones  used  in  structures. 

Expansion  and  contraction  due  to  changes  in  temperature  create 
an  almost  continual  tendency  to  motion  among  the  particles  of 
the  stone,  an  effect  which  is  felt  mainly  at  the  exposed  surfaces 


60  STONE  MASONRY 

where  expansions  are  very  unequal,  and  may  cause  the  scaling  of 
the  surface  layers.  Surfaces  exposed  to  the  direct  rays  of  the  sun 
are  most  affected  from  this  cause.  In  a  number  of  instances,  scal- 
ing of  the  surfaces  on  the  south  side  of  buildings  has  been  observed, 
when  the  less  exposed  sides  were  free  from  it. 

Frost  Action. — When  stone  saturated  with  water  is  frozen,  the 
expansion  of  the  liquid  in  freezing  causes  a  heavy  internal  pressure, 
which  may  be  greater  than  the  tenacity  of  the  stone.  In  the  climate 
of  the  Northern  United  States  this  is  commonly  one  of  the  most 
active  causes  of  disintegration  of  building  stones,  and  the  ability 
to  resist  frost  action  is  of  chief  importance.  The  results  of  the  action 
of  frost  on  a  stone  depend  upon  the  porosity  of  the  stone  and  upon 
the  texture  and  toughness  of  the  material. 

Granite  usually  absorbs  not  more  than  1  per  cent  of  water,  and 
is  not  often  appreciably  affected  by  frost.  Sandstones  and  lime- 
stones may  absorb  from  about  2  to  12  or  even  15  per  cent.  Ordi- 
narily, a  good  stone  that  does  not  absorb  more  than  4  or  5  per  cent 
of  water  may  be  expected  to  stand  frost  well.  Some  more  porous 
stones  have  also  shown  well  in  use.  A  porous  stone  of  coarse  texture 
is  more  apt  to  resist  frost  action  than  one  of  fine  texture.  Moisture 
escapes  more  readily  and  the  stone  is  less  likely  to  be  saturated 
when  frozen. 

Fire  Resistance. — Any  building  stone  may  be  injured  if  subjected 
to  high  heat  as  in  the  case  of  serious  fires.  This  injury  is  intensified 
by  contact  of  water  when  so  heated.  Unequal  expansions  and  sud- 
den surface  contractions  are  likely  to  cause  internal  stresses  beyond 
the  strength  of  the  stone. 

Granites  are  apt  to  split  and  spall  badly  on  the  surface  and 
usually  show  poor  fire-resisting  qualities.  Limestones  usually  resist 
fire  better  than  granite  until  the  heat  becomes  sufficient  to  drive 
off  the  carbonic  acid.  At  high  heats  they  are  destroyed.  When 
suddenly  cooled  by  water,  limestone  is  likely  to  spall  badly.  Sand- 
stones usually  withstand  fires  better  than  other  building  stones, 
sometimes  coming  through  severe  fires  without  serious  injury.  They 
are,  however,  likely  to  spall  and  crack  under  the  combined  action 
of  a  hot  fire  and  water. 

Chemical  Agencies. — Rock  to  be  durable  in  use  as  building  stone 
must  be  capable  of  resisting  changes  due  to  the  presence  of  water 
and  gases  in  the  atmosphere. 

Certain  ingredients  in  the  rock  may  be  soluble  in  water  carrying 
acids  in  solution;  limestones  commonly  weather  in  this  way,  the 
carbonate  of  lime  being  somewhat  soluble  in  water  containing  car- 


BUILDING  STONE  61 

bonic  or  sulphurous  acid,  hence  these  stones  are  usually  liable  to 
surface  deterioration  in  cities.  The  extent  of  such  deterioration 
is  greater  for  the  more  absorbent  stones. 

Building  stone  may  sometimes  be  discolored  by  the  oxidation 
of  pyrite  or  other  iron  compounds  in  its  surface.  This  may  or  may 
not  be  an  injury  to  the  appearance  of  the  structure.  Pyrite  is  apt 
to  cause  rusty  blotches  which  are  objectionable,  although  when, 
evenly  and  finely  distributed  through  sandstone  the  result  is  some- 
times enhances  its  appearance.  Sandstones  in  which  iron  oxide  is 
the  cementing  medium  are  often  changed  in  -color  by  oxidation. 
Siliceous  sandstones  are  not  affected  in  this  manner. 

Seasoning  of  Stone. — All  stone  is  improved  by  being  allowed 
to  stand  and  dry  out  before  being  used  in  construction,  the  evapo- 
ration of  the  quarry  water  being  accompanied  by  hardening  of  the 
stone,  and  the  formation  of  a  crust  upon  the  surface.  In  most  cases 
this  indurating  effect  is  comparatively  small,  but  some  soft  lime- 
stones and  sandstones,  which  are  easily  cut  and  weak  when  first 
quarried,  soon  acquire  considerable  hardness  and  strength,  the  sup- 
position being  that  the  quarry  water  contains  a  small  amount  of 
cementing  material  which  is  deposited  in  the  pores  of  the  stone  upon 
the  evaporation  of  the  water.  For  this  reason  the  cutting  of  the 
stone  should  be  done  before  the  seasoning  has  taken  place,  in  order 
that  the  surface  skin  may  not  be  broken.  This  is  particularly  the 
case  where  elaborate  dressing  or  carving  is  to  be  done. 

Tests  for  Durability. — Observations  of  the  stone  where  it  has 
been  used  in  construction  or  where  it  has  been  long  exposed  in  the 
quarry  is  the  best  means  of  determining  the  probable  durability  of 
a  stone.  Stone  frequently  varies  considerably  in  character  in  dif- 
ferent parts  of  the  same  quarry,  and  this  must  be  taken  into  account 
in  the  selection. 

There  are  no  standard  tests  for  durability.  A  number  of  tests 
have  been  proposed  and  sometimes  applied  for  comparisons  of  stones, 
but  there  is  no  standard  to  which  they  may  be  referred. 

Absorption  Tests. — Tests  to  determine  the  amount  of  water 
absorbed  by  stone  are  sometimes  made.  A  stone  absorbing  little 
water  is  less  likely  to  be  injured  by  frost  or  atmospheric  gases  than 
one  absorbing  water  freely;  in  making  this  test,  it  is  usual  to  dry 
the  stone  at  100°  C.  until  it  ceases  to  lose  weight,  then  soak  the  stone 
for  twenty-four  hours  in  water  and  weigh  again. 

Weight  of  water  absorbed  X 100 

The  percentage  of  absorption  =  Weight  of  dry  stone 

The  method  recommended  for  brick  (see  Section  59)  may  also 


62  STONE  MASONRY 

be  employed  for  stone,  although  there  is  no  standard  for  comparison 
of  the  results. 

Frost  Tests. — Tests  of  the  effect  upon  a  stone  sample  of  repeatedly 
freezing  and  thawing  it,  while  saturated,  have  sometimes  been 
made.  About  twenty  repetitions  are  usual,  and  the  loss  of  weight 
or  the  loss  in  compressive  strength  of  samples  is  measured.  This 
test  requires  considerable  time  and  a  means  of  producing  low  tem- 
peratures. The  differences  obtained  are  usually  very  small,  and 
not  easy  to  evaluate. 

Another  test  intended  to  simulate  the  effects  of  freezing  is  known 
as  the  Brard  test,  which  consists  in  boiling  the  specimen  in  a  con- 
centrated solution  of  sulphate  of  soda,  then  exposing  it  to  the  air, 
and  observing  the  effects  as  the  salt  crystallizes  in  the  pores  of  the 
stone.  This  is  much  more  severe  than  the  ordinary  freezing  test, 
and  may  be  partly  due  to  chemical  action. 

Add  Test. — Samples  of  the  stone  are  sometimes  immersed  in 
weak  solutions  of  hydrochloric  and  sulphuric  acid,  to  determine  the 
presence  of  soluble  material,  by  noting  the  loss  of  weight  after  several 
days.  Exposure  to  an  atmosphere  of  carbonic  acid,  or  oxygen,  is 
sometimes  employed  and  changes  of  color  observed.  None  of  these 
tests  has  been  definitely  formulated  and  standardized. 

BOOKS  ON  BUILDING  STONE 

Complete  descriptions  of  the  various  building  stones  of  the  United  States, 
with  their  properties  and  uses  may  be  found  in  the  following  books: 
Merrill's  "Stones  for  Building  and  Decoration." 
Ries'  "Building  Stones  and  Clay  Products." 

ART.   11.     STONE   CUTTING 

43.  Tools  for  Stone  Cutting. — The  kinds  of  finish  used  in  dressing 
stone  are  usually  defined  by  mentioning  the  tool  with  which  the 
dressing  is  done.  The  following  definitions  were  recommended  by 
a  committee  of  the  American  Society  of  Civil  Engineers  in  1877, 
and  have  since  been  commonly  employed. 


FIG.  4. — Double-face  Hammer. 

"  The  Double-face  Hammer  (Fig.  4)  is  a  heavy  tool  weighing 
from  20  to  30  pounds,  used  for  roughly  shaping  stones  as  they  come 


STONE   CUTTING 


63 


from  the  quarry,  and  knocking  off  projections.     This  is  used  only 
for  the  roughest  work. 

"  The  Face  Hammer  (Fig.  5)  has  one  blunt  and  one  cutting  end, 
and  is  used  for  the  same  purpose  as  the  double-face  hammer  where 
less  weight  is  required.  The  cutting  end  is  used  for  roughly  squaring 
stones,  preparatory  to  the  use  of  finer  tools. 


FIG.  5. — Face  Hammer. 


"  The  cavil  (Fig.  6)  has  one  blunt  and  one  pyramidal  end,  and 
weighs  from  15  to  20  pounds.  It  is  used  in  quarries  for  roughly 
shaping  stones  for  transportation. 


FIG.  6.— Cavil. 

"  The  Pick  (Fig.  7)  somewhat  resembles  the  pick  used  in  digging, 
and  is  used  for  rough  dressing,  mostly  on  sandstone  and  limestone. 
Its  length  varies  from  15  to  24  inches,  the  thickness  at  the  eye  being 
about  two  inches. 


FIG.  7.— Pick. 

"  The  Axe  or  Pean  Hammer  (Fig.  8)  has  two  opposite  cutting 
edges.     It  is  used  for  making  drafts  around  the  arris,  or  edge  of 


64 


STONE   MASONRY 


stones,  and  in  reducing  faces,  and  sometimes  joints  to  a  level.  Its 
length  is  about  10  inches,  and  the  cutting  edges  about  4  inches. 
It  is  used  after  the  point  and  before  the  patent  hammer. 


FIG.  8. — Axe  or  Pean  Hammer. 


"  Tooth  Axe  (Fig.  9)  is  like  the  axe,  except  that  its  cutting  edges 
are  divided  into  teeth,  the  number  of  which  varies  with  the  kind 
of  work  required.  This  tool  is  not  used  on  granite  and  gneiss  cut- 
ting. 


FIG.  9. — Tooth  Axe. 

"  The  Bush  Hammer  (Fig.  10)  is  a  square  prism  of  steel  whose 
ends  are  cut  into  a  number  of  pyramidal  points.  The  length  of  the 
hammer  is  from  4  to  8  inches,  and  the  cutting  face  from  2  to  4  inches 
square.  The  points  vary  in  number  with  the  size  of  the  work  to 
be  done. 


FIG.  10. — Bush  Hammer. 

"  The  Patent  Hammer  (Fig.  11)  is  a  double-headed  tool  so  formed 
as  to  hold  at  each  end  a  set  of  wide  thin  chisels.     The  tool  is  in  two 


FIG.  11  — Patent  Hammer. 


STONE  CUTTING  65 

parts  which  are  held  together  by  the  bolts  which  hold  the  chisels. 
Lateral  motion  is  prevented  by  four  guards  on  one  of  the  pieces. 
The  tool  without  teeth  is  5JX2JX1J  inches.  The  teeth  are  2f 
inches  wide.  Their  thickness  varies  from  TV  to  J  inch.  This  tool 
is  used  for  giving  a  finish  to  the  surface  of  stones. 

"  The  Crandall  (Fig.  12)  is  a  malleable  iron  bar  about  2  feet  long, 
slightly  flattened  at  one  end.  In  this  end  is  a  slot  3  inches  long  and 
f  inch  wide.  Through  this  slot  are  passed  ten  double-headed  points 
of  J-inch  squared  steel,  9  inches  long,  which  are  held  in  place  by  a  key. 


FIG.  12.— Crandall. 

"The  Hand  Hammer,  weighing  from  2  to  5  pounds,  is  used  in  drill- 
ing holes,  and  in  pointing  and  chiseling  the  harder  rocks. 

"  The  Mallet  is  used  where  the  softer  limestones  and  sandstones 
are  to  be  cut. 

"  The  Pitching  Chisel  (Fig.  13a)  is  usually  of  IJ-inch  octagonal 
steel,  spread  on  the  cutting  edge  to  a  rectangle  of  1  by  2J  inches. 
It  is  used  to  make  a  well-defined  edge  to  the  face  of  the  stone,  a  line 
being  marked  on  the  joint  surface  to  which  the  chisel  is  applied,  and 
the  portion  of  the  stone  outside  of  the  line  broken  off  by  a  blow  with 
the  hand  hammer  on  the  head  of  the  chisel. 


V  V 


V  L 


CJ  V 


bed 
FIG.  13. — Chisels  and  Points. 


"  The  Point  (Fig.  136)  is  made  of  round  or  octagonal  rods  of  steel 
from  |  to  1  inch  in  diameter.     It  is  made  about  12  inches  long,  with 


66 


STONE  MASONRY 


one  end  brought  to  a  point.  It  is  used  until  its  length  is  reduced 
to  about  5  inches.  It  is  employed  for  dressing  off  the  irregular  sur- 
faces of  stones,  either  for  a  permanent  finish  or  preparatory  to  the 
use  of  the  axe.  According  to  the  hardness  of  the  stone,  either  the 
hand  hammer  or  the  mallet  is  used  with  it. 

"  The  Chisel  (Fig.  13c)  of  round  steel  J  to  f  inch  in  diameter  and 
about  10  inches  long,  with  one  end  brought  to  a  cutting  edge  from 
J  to  2  inches  wide,  is  used  for  cutting  drafts  or  margins  on  the  faces 
of  stones. 

"  The  Tooth  Chisel  (Fig.  13d)  is  the  same  as  the  chisel  except 
that  the  cutting  edge  is  divided  into  teeth.  It  is  used  only  on  mar- 
bles and  sandstones. 

"The  Splitting  Chisel  (Fig.  13c)  is  used  chiefly  on  the  softer 
stratified  stones,  and  sometimes  on  fine  architec- 
tural carvings  in  granite. 

"  The  Plug,  a  truncated  wedge  of  steel,  and 
the  Feathers,  of  half-rounded  malleable  iron  (Fig. 
14),  are  used  in  splitting  unstratified  stone.  A  row 
of  holes  is  made  with  the  drill  (Fig.  15)  on  the  line 
on  which  fracture  is  to  be  made;  in  each  of  these 


FIG.  15.— Drills. 


holes  two  feathers  are  inserted  and  the  plugs  are  driven  in  between 
them.  The  plugs  are  then  gradually  driven  home  by  light  blows  of 
the  hand  hammer  on  each,  in  succession  until  the  stone  splits." 

44.  Methods  of  Finishing  the  Surfaces. — "All  stones  used  in 
building  are  divided  into  three  classes,  according  to  the  finish  of  the 
surface,  viz. : 

"  1.  Rough  stones  that  are  used  as  they  come  from  the  quarry. 

"  2.  Stones  roughly  squared  and  dressed. 

"  3.  Stones  accurately  squared  and  finely  dressed. 

"  In  practice  the  line  of  separation  between  them  is  not  very 
distinctly  marked,  but  one  class  merges  into  the  next. 

"  Unsquared  Stones. — This  class  covers  all  stones  which  are  used 
as  they  come  from  the  quarry,  without  other  preparation  than  the 
removal  of  very  acute  angles  and  excessive  projections  from  the 
figure.  The  term  backing,  which  is  often  applied  to  this  class  of 


STONE  CUTTING 


67 


stone,  is  inappropriate,  as  it  properly  designates  material  used  in  a 
certain  relative  position  in  the  wall,  whereas  stones  of  this  kind 
may  be  used  in  any  position. 

"  Squared  Stones. — This  class  covers  all  stones  that  are  roughly 
squared  and  roughly  dressed  on  beds  and  joints.  The  dressing  is 
usually  done  with  the  face  hammer  or  axe,  or,  in  soft  stones,  with  the 
tooth  hammer.  In  gneiss,  it  may  sometimes  be  necessary  to  use 
the  point.  The  distinction  between  this  class  and  the  third  lies  in 
the  degree  of  closeness  of  joints.  Where  the  dressing  on  the  joints 
is  such  that  the  distance  between  the  general  planes  of  the  surfaces 
of  adjoining  stones  is  J  inch  or  more  the  stones  properly  belong  to 
this  class. 

"  Three  subdivisions  of  this  class  may  be  made,  depending  on 
the  character  of  the  face  of  the  stones. 

"(a)  Quarry-faced  stones  are  those  whose  faces  are  left  untouched 
as  they  come  from  the  quarry. 

"(b)  Pitch-faced  stones  are  those  on  which  the  arris  is  clearly 
defined  by  a  line  beyond  which  the  rock  is  cut  away  by  the  pitching 
chisel,  so  as  to  give  edges  that  are  approximately  true  (Fig.  16). 


FIG.  16.— Pitch-faced  Squared  Stone. 


FIG.  17.— Drafted  Stone. 


"  Drafted  Stones  are  those  on  which  the  face  is  surrounded  by  a 
chisel  draft,  the  space  within  the  draft  being  left  rough  (Fig.  17). 
Ordinarily,  however,  this  is  done  only  on  stones  in  which  the  cutting 
of  the  joints  is  such  as  to  exclude  them  from  this  class. 

"  In  ordering  stones  of  this  class,  the  specifications  should  always 
state  the  width  of  the  bed  and  end  joints  which  are  expected,  and 
also  how  far  the  surface  of  the  face  may  project  beyond  the  plane 
of  the  edge.  In  practice,  the  proportion  varies  from  1  to  6  inches. 
It  should  also  be  specified  whether  or  not  the  faces  are  to  be  drafted. 

"  Cut  Stones. — This  class  covers  all  squared  stones  with  smoothly 
dressed  beds  and  joints.  As  a  rule,  all  the  edges  of  cut  stones  are 
drafted,  and  between  the  drafts  the  stone  is  smoothly  dressed.  The 
face,  however,  is  often  left  rough  where  the  construction  is  massive. 

"  In  architecture,  there  are  a  great  many  ways  in  which  the  faces 


68 


STONE  MASONRY 


of  cut  stone  may  be  dressed,  but  the  following  are  those  which  will 
usually  be  met  with  in  engineering  work. 

"  Rough-pointed. — When  it  is  necessary  to  remove  an  inch  or 
more  from  the  face  of  a  stone,  it  is  done  by  the  pick  or  heavy  point 
until  the  projections  vary  from  J  inch  to  1  inch.  The  stone  is  then 
said  to  be  rough-pointed.  (Fig.  18.) 


FIG.  18. — Rough-pointed. 


FIG.  19.— Fine-pointed. 


"  Fine-pointed. — If  a  smoother  finish  is  desired,  rough-pointing 
is  followed  by  fine-pointing,  which  is  done  with  a  fine  point.  Fine- 
pointing  is  used  only  where  the  finish  made  by  it  is  to  be  final,  and 
never  as  a  preparation  for  a  final  finish  by  another  tool. 

"  Crandalled. — This  is  only  a  speedy  method  of  pointing,  the 
effect  being  the  same  as  fine-pointing,  except  that  the  dots  on  the 
stone  are  more  regular.  The  variations  of  level  are  about  J  inch, 
and  the  rows  are  made  parallel.  When  other  rows  at  right  angles 
to  the  first  are  introduced,  the  stone  is  said  to  be  cross-crandalled. 


FIG.  20.— Crandalled. 


PIG.  21. — Axed  or  Pean-Hammered. 


"  Axed  or  Pean-Hammered  and  Patent- Hammered. — These  two 
vary  only  in  the  degree  of  smoothness  of  the  surface  which  is  pro- 
duced. The  number  of  blades  in  a  patent  hammer  varies  from  six 
to  twelve  to  the  inch;  and  in  precise  specifications,  the  number  of 
cuts  to  the  inch  must  be  stated,  such  as  6-cut,  8-cut,  10-cut,  12-cut. 
The  effect  of  axing  is  to  cover  the  surface  with  chisel  marks,  which 
are  made  parallel  as  far  as  practicable.  Axing  is  a  fine  finish. 
(Fig.  21.) 

"  Tooth-axed. — The  tooth-axe  is  practically  a  number  of  points, 
and  leaves  the  surface  of  the  stone  in  the  same  condition  as  fine- 
pointing.  It  is  usually,  however,  only  a  preparation  for  bush- 
hammering,  and  the  work  is  done  without  regard  to  effect,  as  long 
as  the  surface  of  the  stone  is  sufficiently  leveled. 


STONE  CUTTING 


69 


"  Bush-hammered— The  roughness  of  the  stone  is  pounded  off 
by  the  bush  hammer,  and  the  stone  is  then  said  to  be  bushed.  (Fig. 
22.)  This  kind  of  finish  is  dangerous  on  sandstone,  as  experience 
has  shown  that  sandstone  thus  treated  is  very  apt  to  scale.  In 
dressing  limestone  which  is  to  have  a  bush-hammered  finish,  the 
usual  sequence  of  operations  is:  (1)  rough-pointing,  (2)  tooth- 
axing,  (3)  Bush-hammering. 


FIG.  22. — Bush-Hammered. 


FIG.  23. — Diamond  Panel. 


"  Rubbed. — In  dressing  sandstone  and  marble,  it  is  very  common 
to  give  the  stone  a  plane  surface  at  once  by  the  use  of  the  stone  saw. 
Any  roughnesses  left  by  the  saw  are  removed  by  rubbing  with  grit 
or  sandstone.  Such  stones  therefore  have  no  margins,  They  are 
frequently  used  in  architecture  for  string  courses,  lintels,  door-jams, 
etc.,  and  they  are  also  well  adapted  for  use  in  facing  the  walls  of 
lock-chambers  and  in  other  locations  where  a  stone  surface  is  liable 
to  be  rubbed  by  vessels  or  other  moving  bodies. 

"Diamond  Panels. — Sometimes  the  space  between  the  margins 
is  sunk  immediately  adjoining  them,  and  then  rises  gradually  until 
the  four  planes  form  an  apex  at  the  middle  of  the  panel.  In  general, 
such  panels  are  called  diamond  panels,  and  the  one  just  described 
(Fig.  23)  is  called  a  sunk  diamond  panel.  When  the  surface  of  the 
stone  rises  gradually  from  the  inner  lines  of  the  margins  to  the  middle 
of  the  panel,  it  is  called  a  raised  diamond  panel.  Both  kinds  of  finish 
are  common  on  bridge-quoins  and  similar  work.  -The  details  of 
this  method  should  be  given  in  the  specifications." 

The  following  classification  of  the  surface  finish  for  stone  used 
in  masonry  is  given  by  the  American  Railway  Engineering  Associ- 
ation: 1 

Dressing. — The  finish  given  to  the  surface  of  stones  or  concrete. 

Smooth. — Having  surface  the  variations  of  which  do  not  exceed  YQ  inch  from 
from  the  pitch  line. 

Fine-Pointed. — Having  irregular  surface,  the  variations  of  which  do  not 
exceed  \  inch  from  the  pitch  line. 

Rough  Pointed. — Having  irregular  surface,  the  variations  of  which  do  not 
exceed  J  inch  from  the  pitch  line. 

1  Manual,  American  Railway  Engineering  Association,  1915. 


70 


STONE   MASONRY 


Scribbled. — Having  irregular  surface,  the  variations  of  which  do  not  exceed 
f  inch  from  the  pitch  line. 

Rock-Faced. — Presenting  irregular  -projecting  face,  without  indications  of 
tool  mark. 

45.  Cutting  by  Machinery. — In  large  yards  and  large  building 
operations  much  of  the  shaping  and  dressing  of  stone  is  done  by 
machinery.  Portable  machines  using  pneumatic  tools  are  frequently 
employed,  such  as  pneumatic  hammers,  drills,  and  chisels,  which 
dress  the  stone  in  much  the  same  manner  as  hand  tools.  The 
machines  commonly  employed  also  include  saws  adapted  to  all 
classes  of  stone — cutters  for  rough  surfacing,  planers  for  more  accu- 
rate surfacing,  and  rubbing  machines  for  grinding  and  polishing. 
The  details  of  these  machines  and  the  character  of  the  tools  used 
with  them  vary  with  the  nature  of  the  stone  to  be  worked. 

In  dimension  stone  and  trimming  work,  drawings  and  dimen- 
sions for  shaping  the  stones  are  provided,  and  the  stones  are  usually 
cut  at  the  yard  and  shipped  to  the  point  of  use  ready  to  place. 


ART.   12.     WALLS   OF   STONE   MASONRY 

46.  Classification  of  Masonry. — Stone  work  is  commonly  divided 
into  two  general  classes;  ashlar  and  rubble,  depending  upon  the 
degree  of  care  exercised  in  cutting  the  stone  and  the  closeness  of  the 
joints. 

Ashlar  masonry  is  that  in  which  the  joints  are  not  more  than 
\  inch  thick.  The  term  ashlar  is  also  sometimes  extended  to  include 
masonry  of  squared  stones  in  which  the  joints  are  not  so  accurately 
dressed,  but  this  is  not  usual. 

Ashlar  masonry  may  be  divided  according  to  the  arrangement 
of  the  stones  into : 

Coursed  ashlar,  sometimes  called  Range  masonry  (Fig.  24), 
arranged  in  courses  of  uniform  thickness. 


J L 


B 


FIG.  24.— Coursed  Ashlar. 


FIG.  25. — Broken  Ashlar. 


Broken  ashlar,  or  Random  ashlar,  in  which  the  stones  are  not 
arranged  in  courses  (Fig.  25). 


WALLS  OF  STONE  MASONRY 


71 


Broken-coursed  or  Random-coursed  ashlar,  in  which  broken  ashlar 
work  is  arranged  in  more  or  less  continuous  courses,  or  masonry 
laid  in  parallel  but  not  continous  courses. 

In  the  best  cut-stone  work,  as  used  by  architects  for  public 
buildings  in  the  cities,  the  joints  may  not  be  more  than  J  inch  thick, 
while  in  first-class  masonry  in  important  engineering  construction 
joints  from  J  to  J  inch  are  usually  allowed.  When  the  thickness 
of  courses  and  length  of  stones  in  ashlar  masonry  are  specified,  the 
work  is  known  as  dimension  stone  masonry. 

The  exposed  surfaces  of  ashlar  masonry  may  be  finished  by  any 
of  the  methods  in  the  preceding  section,  and  the  masonry  is  fre- 
quently classified  as  pitch-faced  ashlar,  drafted-stone  ashlar,  or  cut 
stone  masonry,  which  includes  all  of  the  more  accurate  methods  of 
dressing;  pointing,  bush-hammering,  axing,  etc.  Pitch-faced 'and 
drafted-stone  work  is  often  called  rock-faced  ashlar. 

Rubble  masonry  is  that  which  is  not  dressed  or  laid  with  sufficient 
accuracy  to  be  classed  as  ashlar,  and  may  include  stones  roughly 
squared  or  those  of  irregular  shapes. 

Rubble  masonry  is  usually  uncoursed,  but  sometimes  is  leveled 
off  into  courses  at  specified  heights,  and  is  then  known  as  coursed 
rubble.  Fig.  26  shows  the  face  of  a  wall  of  ordinary  uncoursed  rubble. 


FIG.  26. — Uncoursed  Rubble. 


FIG.  27.— Random  Rubble. 


Fig.  27  shows  a  type  of  rubble  work  sometimes  used  in  building  con- 
struction, in  which  hammer-dressed  joints  are  more  accurately  fitted 
on  the  face  of  the  wall.  Joints  i  to  J  inch  may  be  used  in  such  work. 
This  is  sometimes  called  "  Russian  Bond  "  and  is  usually  rock  faced 
work. 

Dry  Masonry. — Masonry  of  rough  stone  without  the  use  of 
mortar  is  sometimes  employed  and  is  known  as  dry  masonry.  Such 
walls  are  frequently  used  for  railway  culverts  and  similar  purposes. 
When  stone  is  roughly  placed  about  the  bases  of  piers  or  abutments, 
or  on  the  banks  of  streams  to  prevent  erosion,  it  is  commonly  called 
riprap. 


72  STONE  MASONRY 

Squared-Stone  Masonry  is  a  term  frequently  used  to  indicate  a 
class  of  masonry  between  ashlar  and  rubble.  When  this  classi- 
fication is  used,  it  commonly  includes  masonry  of  squared  stones, 
with  joints  from  \  to  1  inch  thick,  and  the  term  rubble  is  limited 
to  the  use  of  irregular  and  unsquared  material. 

Trimmings. — In  architectural  work,  an  additional  classification 
is  sometimes  employed  to  designate  stone  used  for  special  purposes, 
such  as  moldings,  sills,  caps,  etc.  These  usually  require  cutting  to 
specified  dimensions  and  close  joints. 

47.  Parts  of  a  Masonry  Wall. — The  exposed  surface  of  a  masonry 
wall  is  called  its  face,  while  the  interior  surface  is  known  as  the 
back  of  the  wall. 

Batter  is  the  slope  of  the  surface  of  a  wall,  stated  as  a  ratio  of 
horizontal  to  vertical  dimension.  The  walls  of  buildings  usually 
have  no  batter.  Retaining  walls,  bridge  piers,  and  other  heavy 
structures  for  carrying  loads,  are  commonly  given  a  batter  on  the 
face.  This  gives  an  appearance  of  strength  and  stability  to  the  wall. 

Coping  is  a  course  of  stone  on  top  of  the  wall  to  protect  it  and 
give  a  finished  appearance.  The  coping  usually  projects  a  few 
inches  over  the  surface  of  the  wall. 

Courses. — A  horizontal  layer  of  stones  in  the  wall  is  called  a 
course,  the  arrangement  of  courses  in  a  wall  being  determined  by 
the  character  of  the  material  and  the  appearance  desired.  When 
the  stone  may  be  readily  obtained  in  blocks  of  uniform  thickness 
an  arrangement  in  courses,  with  the  thickest  courses  at  the  bottom, 
gives  an  appearance  of  stability,  and  is  common  practice  in  engineer- 
ing structures.  In  architectural  work,  the  arrangement  of  courses 
may  be  made  to  accord  with  other  features  of  the  design  of  the  struc- 
ture. 

Facing  and  Backing. — The  stones  which  form  the  face  of  the 
wall  are  called  facing,  while  those  forming  the  back  of  the  wall  are 
called  backing.  In  the  construction  of  walls,  the  facing  and  backing 
are  commonly  of  different  classes  of  masonry.  An  ashlar  facing 
is  frequently  joined  to  a  rubble  or  concrete  backing. 

In  heavy  walls  the  masonry  of  the  interior  of  the  walls,  between 
the  facing  and  backing,  is  known  as  filling,  and  this  may  sometimes 
be  different  from  either  the  facing  or  backing.  In  constructing 
walls,  the  facing  and  backing  should  always  be  well  bonded,  so  that 
the  whole  acts  together  in  supporting  loads  or  resisting  pressures. 

Headers  and  Stretchers. — A  stone  whose  greatest  dimension  lies 
perpendicular  to  the  face  of  the  wall  is  called  a  header;  one  whose 
greatest  dimension  is  parallel  to  the  face  of  the  wall  is  a  stretcher. 


WALLS  OF  STONE   MASONRY 


73 


The  bond  of  the  masonry  in  the  wall  is  secured  by  proper  arrange- 
ment of  headers  and  stretchers.  The  vertical  joints  in  adjoining 
courses  should  not  be  too  nearly  in  the  same  plane.  A  stone  in  any 
course  should  break  joints  with  the  stones  in  the  course  below  by 
a  distance  at  least  equal  to  the  depth  of  the  course.  The  strongest 
bond  is  obtained  by  using  an  equal  number  of  headers  and  stretchers 
in  the  face  of  the  wall,  a  header  being  placed  over  the  middle  of 
each  stretcher  as  shown  in  Fig.  24. 

In  the  use  of  coursed  ashlar  facing,  the  rubble  filling  and  back- 
ing is  usually  also  coursed  at  the  same  height  as  the  ashlar.  Some- 
times in  massive  work  the  filling  may  be  constructed  of  irregular 
uncoursed  rubble.  Usually,  however,  concrete  would  be  used  in 
such  work  instead  of  rubble. 

In  the  walls  of  buildings  with  ashlar  facings,  the  rubble  backing 
is  laid  in  courses  with  the  ashlar  and  occasional  headers  are  run 
through  the  wall  as  shown  in  Fig.  28.  Brick  backing  is  commonly 
used  for  such  work  and  is  usually  preferable  to  rubble.  (Fig,  29.) 


H-i 


FIG.  28. 


FIG.  29. 


In  building  work,  thin  ashlar,  2  to  4  inches  thick,  is  sometimes 
employed  as  a  veneer  on  the  exterior  of  a  wall  of  rubble  or  brick; 
this  is  frequently  done  in  marble  buildings.  The  veener  is  tied  to 
the  backing  by  iron  clamps,  and  occasional  belt  courses  of  wider 
stones,  extending  6  or  8  inches,  into  the  filling  give  support  to  the 
ashlar. 

Dowels  and  Cramps. — For  the  purpose  of  strengthening  the  bond 
where  great  resistance  is  required,  dowels  or  cramps  are  often  em- 
ployed. A  dowel  is  a  straight  bar  of  iron  which  enters  a  hole  in  the 
upper  side  of  one  stone  and  also  a  hole  in  the  lower  side  of  the  stone 
above.  A  cramp  is  a  bar  of  iron  with  ends  bent  at  right  angles  to 
the  length  of  the  bar,  the  ends  entering  holes  in  the  tops  of  adjacent 
stones. 

48.  Setting  Stonework. — The  layers  of  mortar  between  stones 


74  STONE  MASONRY 

are  called  joints.  The  horizontal  joints  are  commonly  called  beds 
or  bed  joints. 

The  kind  of  mortar  used  in  stonework  depends  upon  the  character 
of  the  work.  In  engineering  structures,  1  to  2  or  1  to  3,  Portland 
cement  mortar  is  usually  employed.  Cement  mortar  stains  many 
stones  and  care  must  be  used  in  architectural  work  to  prevent  injury 
to  appearance  of  the  stone  surface  from  this  cause.  This  may 
often  be  effected  by  keeping  the  bed  and  joint  mortar  back  from 
the  face  and  using  non-staining  mortar  for  pointing.  The  bed 
joint  of  ashlar  stones  should  be  carefully  dressed  to  a  plane  surface 
in  order  that  the  stone  may  bear  evenly  upon  the  bed.  These  joints 
are  sometimes  cut  slightly  concave  to  make  them  easier  to  set  with 
close  joints  at  the  surface,  which  brings  the  loads  upon  the  edges 
of  the  stone  with  danger  of  chipping  the  edges. 

The  vertical  joints  in  ashlar  facing  should  be  carefully  dressed 
to  a  depth  of  several  inches  from  the  face  of  the  wall,  but  do  not 
need  to  be  accurately  dressed  the  full  depth  of  the  stone.  The 
backs  of  the  ashlar  stones  may  be  laid  as  rubble  without  cutting. 
The  arrangement  of  headers  and  stretchers  in  the  rubble  backing 
should  be  the  same  as  in  the  ashlar  facing  to  secure  good  bond  through- 
out the  wall. 

Placing  Stone. — All  stones  should  be  set  in  a  full  bed  of  mortar. 
The  mortar  bed  should  be  prepared  and  the  stone  lowered  upon  it 
without  disturbing  stones  already  set.  The  stone  must  not  be  slid 
upon  the  bed  so  as  to  scrape  away  the  mortar.  Stones  too  large 
to  be  handled  by  one  man  are  placed  with  a  derrick,  and  are  settled 
in  place  with  light  blows  from  a  hammer.  No  cutting  or  trimming 
of  stone  after  placing  is  allowable;  the  stone  must  be  fitted  to  its 
place  before  spreading  the  mortar. 

In  the  construction  of  rubble  masonry,  less  care  may  be  taken 
in  the  exact  placing  of  the  stones,  but  it  is  highly  important  that 
all  the  joints  be  completely  filled.  The  strength  of  the  masonry 
depends  upon  the  stone  having  full  bearing  on  the  mortar  at  all 
points.  The  interstices  between  large  stones  in  rough  rubble  are 
filled  by  driving  stone  chips  into  the  mortar. 

Stratified  stones  should  always  be  set  upon  their  natural  beds, 
and  not  set  on  edge. 

Dimensions  of  Stones. — A  rule  frequently  used  is  that  the  width 
of  a  stone  shall  not  be  less  than  its  height.  The  length  of  the  stone, 
to  avoid  danger  from  cross-breaking,  in  well-laid  masonry,  may  be 
about  three  times  the  thickness  for  the  weaker  stones,  and  about 
five  times  the  thickness  for  the  stronger  ones. 


WALLS  OF  STONE  MASONRY  75 

Pointing. — In  laying  masonry  it  is  not  feasible  to  make  well- 
filled,  smooth  joints  at  the  face  of  the  wall.  It  is  usual,  therefore, 
after  the  masonry  has  been  laid,  to  clear  out  the  joint  to  a  depth  of 
about  an  inch  and  refill  with  special  mortar.  This  is  called  pointing 
the  masonry.  If,  in  placing  the  masonry,  the  mortar  in  the  joints 
is  not  brought  quite  to  the  face  of  the  wall,  the  labor  of  pointing 
may  be  somewhat  lessened. 

The  joint  is  cleared  and  brushed  out  to  a  depth  of  at  least  an 
inch  and  well  moistened  before  applying  the  pointing.  The  mortar 
is  then  applied  with  a  small  trowel,  squeezed  in,  and  smoothed 
with  a  special  tool  called  a  jointer,  which  is  provided  with  an  edge 
to  form  the  kind  of  finish  desired.  There  are  a  number  of  ways  of 
finishing  joints,  of  which  the  most  common  are  shown  in  Fig.  30. 

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FIG.  30. — Methods  of  Finishing  Joints. 

The  best  pointing  mortar  is  usually  composed  of  Portland  cement 
and  sand,  1  to  1.  Coloring  matter  is  added  when  needed.  The 
mortar  is  used  quite  dry,  like  damp  earth.  When  the  face  of  the 
stone  would  be  stained  by  Portland  cement,  a  putty  made  of  lime, 
plaster  of  paris,  and  white  lead  is  sometimes  employed.  Various 
non-staining  cements  are  also  available. 

49.  Trimmings. — In  the  erection  of  masonry  structures,  certain 
special  parts  are  ordinarily  required  to  be  of  cut  stone,  which  must 
be  of  definite  form  and  dimension.  These  trimmings  have  to  do 
with  the  ornamentation  of  the  structure,  finishing  about  openings, 
or  joining  different  types  of  construction. 

Water-tables  with  sloping  surfaces  are  used  at  the  top  of  founda- 
tion walls,  where  they  join  the  narrower  upper  walls. 

Copings,  cornices,  window  sills,  and  sometimes  belt-courses  pro- 
ject beyond  the  surface  of  the  wall;  they  must  have  sufficient  width 
to  be  firmly  held  in  the  wall,  and  to  balance  on  the  wall  in  laying. 
The  projections  should  also  have  upper  surfaces  which  slope  away 
from  the  wall,  and  a  drip  (called  the  wash)  underneath  to  cause 
water  to  drop  off  at  the  outer  edge,  the  drip  being  made  by  cutting 
a  groove  on  the  under  side  of  the  stone. 

When  cut-stone  trimmings  are  used  for  a  brick  wall,  they  should 
be  dimensioned  so  that  they  will  fit  into  the  brickwork  without 
splitting  the  brick. 


76  STONE   MASONRY 

Window  sills  just  the  width  of  the  opening  and  not  built  into 
the  wall  at  the  ends  are  called  slip  sills,  while  those  extending  into 
the  walls  are  called  lug  sills.  The  ends  of  lug  sills  are  rectangular, 
the  sloping  surface  of  the  sill  being  made  the  width  of  the  opening. 
Lug  sills  should  be  bedded  only  at  the  ends  to  prevent  cross-bending 
stresses  due  to  the  weight  of  the  wall. 

When  stone  lintels  are  used  to  span  openings,  care  must  be  taken 
in  selecting  the  stone,  and  making  sure  that  it  has  the  transverse 
strength  necessary  to  carry  the  load.  When  necessary  an  angle 
bar  or  I-beam  may  be  used  to  support  the  lintel,  a  recess  being  cut 
into  the  back  of  the  stone  for  this  purpose. 

50.  Specifications  for  Stone  Masonry. — The  following  general 
requirements  for  stone  masonry  and  special  requirements  for  bridge 
and  retaining  wall  masonry  are  recommended  by  the  American 
Railway  Engineers'  Association  in  their  Manual  for  1915: 

GENERAL  REQUIREMENTS 

Stone. — 3.  Stone  shall  be  of  the  kinds  designated  and  shall  be  hard  and 
durable,  of  approved  quality  and  shape,  free  from  seams  or  other  imperfections. 
Unseasoned  stone  shall  not  be  used  where  liable  to  injury  by  frost. 

Dressing. — 4.  Dressing  shall  be  the  best  of  the  kind  specified. 

5.  Beds  and  joints  or  builds  shall  be  square  with  each  other,  and  dressed 
true  and  out  of  wind.     Hollow  beds  shall  not  be  permitted. 

6.  Stone  shall  be  dressed  for  laying  on  the  natural  bed.     In  all  cases  the 
bed  shall  not  be  less  than  the  rise. 

7.  Marginal  drafts  shall  be  neat  and  accurate. 

8.  Pitching  shall  be  done  to'  true  lines  and  exact  batter. 

Mortar. — 9.  Mortar  shall  be  mixed  in  a  suitable  box,  or  in  a  machine  mixer, 
preferably  of  the  batch  type,  and  shall  be  kept  free  from  foreign  matter.  The 
size  of  the  batch  and  the  proportions  and  the  consistency  shall  be  as  directed 
by  the  engineer.  When  mixed  by  hand  the  sand  and  cement  shall  be  mixed 
dry,  the  requisite  amount  of  water  then  added  and  the  mixing  continued  until 
the  cement  is  uniformly  distributed  and  the  mass  is  uniform  in  color  and  homo- 
geneous. 

Laying. — 10.  The  arrangement  of  courses  and  bond  shall  be  as  indicated 
on  the  drawings,  or  as  directed  by  the  engineer.  Stone  shall  be  laid  to  exact 
lines  and  levels,  to  give  the  required  bond  and  thickness  of  mortar  in  beds  and 
joints. 

11.  Stone  shall  be  cleansed  and  dampened  before  laying. 

12.  Stone  shall  be  well  bonded,  laid  on  its  natural  bed  and  solidly  settled, 
into  place  in  a  full  bed  of  mortar. 

13.  Stone  shall  not  be  dropped  or  slid  over  the  wall,  but  shall  be  placed 
without  jarring  stone  already  laid. 

14.  Heavy  hammering  shall  not  be  allowed  on  the  wall  after  a  course  is  laid. 

15.  Stone  becoming  loose  after  the  mortar  is  set  shall  be  relaid  with  fresh 
mortar. 


WALLS  OF  STONE   MASONRY  77 

16.  Stone  shall  not  be  laid  in  freezing  weather,  unless  directed  by  the  En- 
gineer.    If  laid,  it  shall  be  freed  from  ice,  snow,  or  frost  by  warming.    The  sand 
and  water  used  in  the  mortar  shall  be  heated. 

17.  With  precaution,  a  brine  maybe  substituted  for  the  heating  of  the  mor- 
tar.    The  brine  shall  consist  of  1  pound  of  salt  to  18  gallons  of  water,  when  the 
temperature  is  32°  F.;   for  every  degree  of  temperature  below  32°  F.,  1  ounce 
of  salt  shall  be  added. 

18.  Before  the  mortar  has  set  in  beds  and  joints,  it  shall  be  removed  to  a 
depth  of  not  less  than  1  inch.     Pointing  shall  not  be  done  until  the  wall  is  com- 
plete and  mortar  set;  nor  when  frost  is  in  the  stone. 

19.  Mortar  for  pointing  shall  consist  of  equal  parts  of  sand,  sieved  to  meet 
the  requirements,  and  Portland  cement.     In  pointing,  the  joints  shall  be  wet, 
and  filled  with  mortar,  pounded  in  with  a  "set-in"  or  calking  tool  and  finished 
with  a  beading  tool  the  width  of  the  joint,  used  with  a  straight-edge. 

BRIDGE  AND  RETAINING  WALL  MASONRY,  ASHLAR  STONE 

Bridge  and  Retaining  Wall  Masonry,  Ashlar  Stone. — 20.  The  stone  shall  be 
large  and  well  proportioned.  Courses  shall  not  be  less  than  14  niches  or  more 
than  30  inches  thick,  thickness  of  courses  to  diminish  regularly  from  bottom 
to  top. 

Dressing. — 21.  Beds  and  joints  or  builds  of  face  stone  shall  be  fine-pointed, 
so  that  the  mortar  layer  shall  not  be  more  than  J  inch  thick  when  the  stone  is 
laid. 

22.  Joints  in  face  stone  shall  be  full  to  the  square  for  a  depth  equal  to  at 
least  onte-half  the  height  of  the  course,  but  in  no  case  less  than  12  inches. 

Face  or  Surface. — 23.  Exposed  surfaces  of  the  face  stone  shall  be  rock-faced, 
with  edges  pitched  to  the  true  lines  and  exact  batter.  The  face  shall  not  pro- 
ject more  than  3  inches  beyond  the  pitch  lines. 

24.  Chisel  drafts  1 J  inches  wide  shall  be  cut  at  exterior  corners. 

25.  Holes  for  stone  hooks  shall  not  be  permitted  to  show  in  exposed  surfaces. 
Stone  shall  be  handled  with  clamps,  keys,  lewis,  or  dowels. 

Stretchers. — 26.  Stretchers  shall  not  be  less  than  4  feet  long  with  at  least  one 
and  a  quarter  times  as  much  bed  as  thickness  of  course. 

Headers. — 27.  Headers  shall  not  be  less  than  4  feet  long;  shall  occupy  one- 
fifth  of  face  of  wall;  shall  not  be  less  than  18  inches  wide  in  face;  and  where 
the  course  is  more  than  18  inches  high,  width  of  face  shall  not  be  less  than  height 
of  course. 

28.  Headers  shall  hold  in  heart  of  wall  the  same  size  shown  in  face,  so  arranged 
that  a  header  in  a  superior  course  shall  not  be  laid  over  a  joint,  and  a  joint  shall 
not  occur  over  a  header;  the  same  disposition  shall  occur  in  back  of  wall. 

29.  Headers  in  face  and  back  of  wall  shall  interlock  when  thickness  of  wall 
will  admit. 

30.  Where  the  wall  is  3  feet  thick  or  less,  the  face  stone  shall  pass  entirely 
through.     Backing  shall  not  be  permitted 

Backing. — 31a.  Backing  shall  be  large,  well-shaped  stone,  roughly  bedded 
and  jointed;  bed  joints  shall  not  exceed  1  inch.  At  least  one-half  of  the  back- 
ing stone  shall  be  of  the  same  size  and  character  as  the  face  stone  and  with  parallel 
ends.  The  vertical  joints  in  back  of  wall  shall  not  exceed  2  inches.  The  interior 
vertical  joints  shall  not  exceed  6  inches. 


78  STONE   MASONRY 

Voids  shall  be  throughly  filled  with  concrete,  or  with  spalls,  fully  bedded 
in  cement  mortar. 

316.  Backing  shall  be  of  concrete,  or  of  headers  and  stretchers,  as  specified 
in  paragraphs  26  and  27,  and  heart  of  wall  filled  with  concrete. 

Paragraphs  31a  and  316  are  so  arranged  that  either  may  be  eliminated  accord- 
ing to  requirements. 

32.  Where  the  wall  will  not  admit  of  such  arrangement,  stone  not  less  than 
4  feet  long  shall  be  placed  transversely  in  heart  of  wall  to  bond  the  opposite  sides. 

33.  Where  stone  is  backed  with  two  courses,  neither  course  shall  be  less  than 
8  inches  thick. 

Bond. — Bond  of  stone  in  face,  back,  and  heart  of  wall  shall  not  be  less  than 
12  inches.  Backing  shall  be  laid  to  break  joints  with  the  face  stone  and  with 
one  another. 

Coping. — 35.  Coping  stone  shall  be  full  size  throughout,  of  dimensions  indi- 
cated on  the  drawings. 

36.  Beds,  joints  and  top  shall  be  fine-pointed. 

37.  Location  of  joints  shall  be  determined  by  the  position  of  the  bed  plates 
as  indicated  on  the  drawings. 

Locks. — 38.  Where  required,  coping  stone,  stone  in  the  wings  of  abutments, 
and  stone  on  piers,  shall  be  secured  together  with  iron  cramps  or  dowels,  to  the 
position  indicated  on  the  drawings. 

BRIDGE  AND  RETAINING  WALL  MASONRY,  RUBBLE  STONE 

39.  The  stone  shall  be  roughly  squared  and  laid  in  irregular  courses.     Beds 
shall  be  parallel,  roughly  dressed,  and  the  stone  laid  horizontal  to  the  wall.    Face 
joints  shall  not  be  more  than  1  inch  thick.     Bottom  stone  shall  be  large,  selected 
flat  stone. 

40.  The  wall  shall  be  compactly  laid,  having  at  least  one-fifth  the  surface 
of  back  and  face  headers  arranged  to  interlock,  having  all  voids  in  the  heart  of 
the  wall  thoroughly  filled  with  concrete,  or  with  suitable  stones  and  spalls,  fully 
bedded  in  cement  mortar. 


ART.   13.      STRENGTH   OF  STONE  MASONRY 

51.  Compressive  Strength. — Stone  masonry  varies  widely  in 
strength  according  to  the  character  of  the  construction.  The 
accuracy  with  which  the  joints  are  dressed,  the  strength  of  the  mor- 
tar, the  bonding  of  the  masonry  and  size  of  blocks  of  stone  are  more 
important  than  the  strength  of  the  stone  itself. 

No  experimental  data  are  available  which  show  the  actual  strength 
of  masonry  as  used.  The  mortar  has  usually  much  less  strength 
than  the  stone,  and  in  some  experiments  on  brick  piers,  the  mortar 
seemed  to  squeeze  out,  causing  the  failure  of  the  brick  in  tension. 
The  loads  to  which  masonry  is  ordinarily  subjected  are  much  less 
than  its  actual  strength,  but  when  heavy  loads  are  being  carried 
by  piers  or  arches,  it  is  frequently  necessary  to  proportion  the  sec- 
tion to  the  load. 


STRENGTH  OF  STONE  MASONRY  79 

When  the  masonry  is  of  cut  stone  with  thin  joints  and  Portland 
cement  mortar,  the  strength  of  the  masonry  may  be  proportioned 
to  the  strength  of  the  stone.  For  rubble  with  thick  joints,  the 
strength  of  the  stone  has  no  material  effect  upon  the  strength  of 
the  masonry. 

The  loads  used  in  practice  vary  quite  widely  according  to  the 
views  of  the  designers.  Building  laws  of  the  various  cities  differ 
considerably  in  the  loads  allowed.  The  following  may  be  considered 
as  conservative  values  for  the  limits  of  safe  loading: 

Cut  Stone. — Dressed  stone,  with  joints  not  more  than  f  inch  in 
first  class  Portland  cement  mortar: 

Tons  per 
Square  Foot. 

Granite 50  to  60 

Hard  limestone  or  marble 35  to  40 

Sandstone 25  to  30 

The  siliceous  sandstones  may  have  larger  values,  while  the  soft 
limestones  should  be  reduced. 

For  ashlar  of  good  quality  as  commonly  laid  with  J-inch  joints 
in  Portland  cement: 

Tons  per 
Square  Foot. 

Granite 40  to  45 

Limestone,  hard 35  to  40 

Sandstone 25  to  30 

Rubble. — For  masonry  composed  of  large  blocks  of  squared  stone, 
1-inch  joints,  in  Portland  cement  mortar: 

Tons  per 
Square  Foot. 

Sandstones  or  limestones 10  to  20 

Granite 20  to  30 

Uncoursed  rubble: 

In  cement  mortar 5  to    8 

In  lime  mortar 3  to    5 

For  an  ashlar  pier  whose  height  exceeds  ten  times,  or  a  rubble 
pier  whose  height  exceeds  five  times,  its  least  lateral  dimension,  these 
figures  should  be  reduced.  Piers  of  small  dimensions  carrying 
heavy  loads  should  always  be  of  ashlar.  Rubble  should  not  be 
used  for  less  thicknesses  than  20  to  24  inches  when  it  is  necessary 
to  develop  the  full  strength  of  the  masonry. 

Failures  of  masonry  most  frequently  occur  through  defective 
foundation  or  workmanship.  Masonry,  to  develop  its  full  strength, 


80  STONE  MASONRY 

must  always  be  adequately  supported,  so  that  unequal  pressures 
are  not  produced  through  settlement. 

Weight  of  Masonry. — In  determining  loads^  fit  is  usually  necessary 
to  estimate  the  weight  of  masonry.  This  depends  upon  the  specific 
gravity  of  the  stone  and  the  closeness  of  the  joints.  The  following 
table  gives  approximate  weights  for  the  different  classes  of  stone 
masonry: 

Pounds  per 
Cubic  Foot. 

Limestone,  ashlar 155  to  165 

Limestone,  squared  rubble 145  to  150 

Limestone,  rough  rubble 135  to  140 

Granite,  ashlar 165  to  170 

Granite,  squared  rubble 155  to  160 

Sandstone,  ashlar 135  to  150 

Sandstone,  rubble 120  to  140 

52.  Capstones  and  Templets. — When  loads  are  to  be  transferred 
from  the  ends  of  beams  or  columns  to  masonry  walls  or  piers,  bearing 
blocks  may  be  necessary  properly  to  distribute  the  loads  over  the 
surface  of  the  masonry.  When  used  under  a  column  or  post,  these 
blocks  are  called  capstones;  when  used  in  walls  to  carry  the  ends  of 
beams,  they  are  templets. 

In  placing  bearing  blocks,  the  loads  should  always  be  centered 
on  the  top  of  the  block,  if  possible,  so  as  to  produce  uniform  pressure 
upon  the  masonry  below;  in  all  cases,  the  center  of  pressure  must 
be  within  the  middle  third  of  the  base  to  avoid  a  tendency  to  open 
the  joint  between  the  bearing  block  and  the  masonry,  In  Fig.  31, 


\P 
..lt 1 /,  _„ 


FIG.  31. 

let    P=the  vertical  load  at  center  of  pressure; 

61  =  the  pressure  at  edge  nearest  the  center  of  pressure; 

62  =  the  pressure  at  edge  farthest  from  center  of  pressure ; 
I  =  the  length  of  stone ; 

x  =  distance  from  middle  of  block  to  center  of  pressure; 


STRENGTH  OF  STONE   MASONRY  81 

Zi  =  distance  from  nearest  edge  to  center  of  pressure; 
12  =  distance  from  farthest  edge  to  center  of  pressure ; 
b2  =  width  of  block.  Then, 

Pl+6Px 


bl2         bl2 

and 

4PZ-6P/2     Pl- 
k2  = 


bl2  bl2 

When  s  =  0,  h  =  l/2  and  ki=k2  =  P/lb.  When  x  =  l/6,  Zi  =  Z/3, 
ki  =  2P/lb  and  &2  =  0.  If  x  becomes  greater  than  1/6,  k^  is  negative 
and  a  tension  will  be  developed  in  the  joint  or  it  will  open. 

In  designing  a  bearing  block,  k\  must  not  be  greater  than  the  safe 
load  for  the  masonry.  The  load  is  commonly  brought  on  top  of  a 
bearing  block  through  an  iron  plate,  which  should  have  such  area 
that  the  pressure  will  not  be  more  than  one-tenth  to  one-twelth  of 
•the  crushing  strength  of  the  stone.  The  bearing  block  must  have 
sufficient  thickness  not  to  break  under  the  transverse  load  imposed 
by  the  upward  pressure  of  the  masonry. 

In  designing  a  templet  which  is  to  be  built  into  a  wall,  the  weight 
of  wall  resting  on  the  top  of  the  templet  must  be  included  in  deter- 
mining the  pressure  on  its  base. 

53.  Lintels  and  Corbels. — A  stone  lintel  is  a  beam  of  stone  span- 
ning an  opening  in  a  wall.  The  strength  of  a  lintel  is  determined 
by  the  ordinary  beam  formulas.  The  safe  modulus  of  rupture  may 
be  taken  at  about  one-twelfth  to  one-tenth  of  the  ultimate  modulus 
for  the  stone.  Mean  values  of  the  safe  modulus  of  rupture  are 
about  as  follows:  granite,  180  lbs./in.2;  Limestone,  150;  marble, 
130;  sandstone,  120  lbs./in.2.  There  are,  however,  certain  tough 
sandstones,  specially  adapted  to  this  use,  which  may  be  used  with 
modulus  of  250  to  300  lbs./in.2 

Beams  carrying  live  loads  should  not  rest  upon  stone  lintels. 
When  the  load  upon  a  lintel  is  a  solid  masonry  wall,  it  is  common 
to  assume  that  the  masonry  may  arch  over  the  opening,  so  that 
the  actual  weight  upon  the  lintel  is  only  that  of  a  triangle  whose 
height  is  about  three-quarters  of  the  span.  This  assumes  that 
the  lintel  will  yield  somewhat,  and  be  relieved  of  stress  before  reach- 
ing the  maximum  load.  It  is  quite  possible  that  in  well-built 
masonry,  with  cement  mortar,  the  lintel  might  be  removed  without 
the  wall  above  yielding  at  all.  If,  however,  there  is  no  yielding 
of  the  lintel,  the  pressure  upon  its  upper  surface  may  be  the  same 
as  at  any  other  point  in  the  same  horizontal  plane  of  the  wall. 


82 


STONE   MASONRY 


Beam 


A  corbel  is  a  block  of  stone  extending  beyond  the  surface  of  a 
wall  or  pier  for  the  purpose  of  carrying  the  end  of  a  beam  or  an 
overhanging  wall,  see  Fig.  32.  The  overhang  of  the  corbel  is  a 

cantilever  beam,  which  must  have 
sufficient  section  at  the  surface  of 
the  wall  to  resist  the  bending  moment 
due  to  the  load.  The  corbel  must 
extend  sufficiently  into  the  wall,  to 
give  a  resultant  pressure  within  the 
middle  third  of  the  base  of  the  corbel 
(R  =  P-{-W))  as  in  the  case  of  bearing 
blocks. 

FIG.  32. — Corbels.  Double  corbels  may  be  used  when 

necessary,  each  being  separately  treated 

in  determining  strength.     When  weight  of  wall  above  (W)  is  lack- 
ing, the  corbel  must  be  anchored  to  the  wall  below  by  steel  ties. 


ART.  14.    MEASUREMENT  AND   COST 

54.  Methods  of  Measurement. — In  engineering  work  it  is  usual 
to  estimate  stone  masonry  in  cubic  yards  of  actual  masonry.     When 
parts  of  the  work  are  of  special  character,  requiring  cut-stone  finish, 
special  prices  per  cubic  yard  may  be  given,  or  the  additional  costs 
of  the  cut  surfaces  are  paid  for  by  the  square  yard. 

In  architectural  work  masonry  is  measured  by  the  cubic  yard 
or  by  the  perch.  A  perch  may  be  16  J,  22,  or  25  cubic  feet,  accord- 
ing to  the  custom  of  the  locality  in  which  the  masonry  is  constructed. 
In  the  use  of  the  perch  as  a  unit,  it  is  advisable  to  state  the  number 
of  cubic  feet  to  be  considered  a  perch. 

In  building  work  it  is  common  to  take  outside  measurements 
of  walls,  thus  including  the  corner  masonry  twice;  it  is  also  custom- 
ary to  measure  small  openings  as  solid  wall.  Commonly  openings 
less  than  70  square  feet  are  not  deducted.  In  some  cases  allow- 
ances are  made  for  openings  more  than  6  feet  wide.  Customs  differ 
in  different  parts  of  the  country,  and  it  is  necessary  to  know  the 
local  usage,  unless  the  method  of  measurement  is  stated. 

55.  Cost  of  Stone  Masonry. — So  many  items  are  included  in 
the  cost  of  masonry  and  these  items  vary  so  widely  in  different 
localities  that  it  is  not  feasible  to  give  any  definite  values  to  the 
costs  of  different  kinds  of  work.     The  items  of  cost  include  the  price 
of  the  rough  stone  at  the  quarry,  the  transportation  to  place  of  use, 


MEASUREMENT  AND  COST  83 

dressing  joints  and  faces  of    stone,  mortar  for  joints,  setting  the 
stonework,  and  pointing  the  joints. 

Rough  stones  at  the  quarry  are  commonly  classified  into  rubble 
or  small  stone  and  dimension  stone.  Rubble  stone  includes  the 
more  irregular  stones  and  blocks  suitable  for  small  ashlar.  Dimen- 
sion stone  includes  all  stone  required  to  be  of  particular  sizes  and 
blocks  of  large  dimensions  and  definite  thicknesses,  as  required  for 
coursed  ashlar.  These  classes  vary  according  to  the  kinds  of  stone 
in  the  quarry  and  the  specifications  to  be  met  by  the  stone. 

Rubble  stone  is  commonly  sold  by  the  ton  free  on  board  cars 
at  point  of  delivery.  Prices  for  rubble  stone  delivered  have  varied 
in  various  localities  from  $0.50  to  $2  per  ton,  when  wages  of  quarry- 
men  were  about  $4.50  per*  day  and  common  labor  $1.50.  The  cost 
is  largely  a  matter  of  locality.  A  ton  of  rubble  stone  may  lay  from 
about  16  to  22  cubic  feet  of  masonry. 

Dimension  stone  and  ashlar  in  the  rough  may  cost  from  $0.50 
to  $1.25  per  cubic  foot  for  limestone  or  sandstone  and  $0.75  to  $1.50 
per  cubic  foot  for  granite,  according  to  quality  and  location. 

Cost  of  Stone  Cutting. — The  cost  of  cutting  ashlar  depends  upon 
the  hardness  of  the  stone  and  the  shape  in  which  the  blocks  are 
received.  Some  stratified  stones  require  almost  no  dressing  on  the 
bed  joints,  while  other  stones  need  every  joint  dressed  from  an 
irregular  surface.  With  wages  of  stone  cutters  at  $5  per  day,  the 
following  may  be  considered  average  costs  per  square  foot  for  cutting 
to  J-inch  joints;  granites,  27  to  35  cents;  hard  sandstones  and 
limestones,  20  to  30  cents;  soft  stones,  16  to  22  cents.  Costs  of 
peculiar  face  cuttings  and  of  trimmings  are  so  special  to  particular 
stones  that  they  are  of  little  value  for  general  use.  Sills,  lintels, 
water-tables,  and  copings  are  usually  sold  by  the  lineal  foot. 

The  cost  of  sawing  and  machine  dressing  is  usually  much  less 
than  that  for  hand  dressing,  and  varies  with  the  way  the  stone  is 
handled  and  the  organization  of  the  yard. 

'  Mortar  Required. — The  amount  of  mortar  needed  in  rubble 
masonry  may  vary  from  about  15  to  35  per  cent  of  the  volume  of 
the  masonry.  Rubble  of  squared  stones  with  joints  1  inch  thick 
will  ordinarily  require  15  to  20  per  cent,  according  to  the  sizes  of  the 
stones.  For  random  rubble,  stratified  stones  with  flat  beds  require 
less  than  irregular  stones.  In  the  use  of  irregular  rubble  stones, 
the  careful  use  of  spalls  in  the  larger  joints  reduces  the  amount  of 
mortar  materially,  with  saving  in  cost. 

The  amount  of  mortar  needed  for  ashlar  work  depends  upon  the 
sizes  of  the  stones.  Ordinary  ashlar  with  J-inch  joints  in  courses 


84  STONE  MASONRY 

12  to  20  inches  thick  requires  4  to  7  per  cent  of  mortar;  random 
ashlar  with  smaller  stones  will  require  more,  while  with  large  blocks 
and  thinner  joints  less  will  be  required. 

Cost  of  Laying  Masonry. — The  cost  of  setting  stone  varies  with 
the  size  of  the  job,  the  organization  of  the  work,  and  the  skill  of  the 
masons,  as  well  as  with  the  character  of  the  work  itself.  In  ordinary 
rubble  or  squared-stone  work,  such  as  cellar  walls  or  light  retaining 
walls,  a  mason  should  lay  a  cubic  yard  of  masonry  in  three  or  four 
hours.  A  helper  to  two  masons  or  a  helper  to  each  mason,  accord- 
ing to  convenience  of  work,  being  required  to  supply  stone  and 
mortar.  With  masons  at  50  cents  an  hour  and  helpers  at  20  cents, 
this  would  cost  from  $1.80  to  $2.80  per  cubic  yard.  In  large  work, 
where  stone  is  handled  by  derricks,  and  rubble  constructed  of  large 
blocks,  the  cost  of  placing  the  stone  is  frequently  reduced  to  $0.85 
to  $1.25  per  cubic  yard.  The  cost  of  setting  ordinary  ashlar  varies 
from  about  $3  to  $5  per  cubic  yard  for  limestone  and  sandstone, 
and  from  $6  to  $9  for  granite. 

The  total  cost  of  masonry  in  place,  made  up  by  so  many  varying 
items,  necessarily  varies  within  wide  limits.  Ordinary  rubble  at 
prices  which  have  existed  within  the  past  few  years  (previous  to  the 
War),  averages  in  cost  from  $5  to  $7  per  cubic  yard.  Rubble  in 
heavy  construction,  usually  granite,  where  the  stone  was  quarried 
on  the  work  and  handled  by  machinery,  has  run  from  $5  to  $11 
per  cubic  yard.  Sandstone  and  limestone  bridge  masonry,  with 
ashlar  facings  and  rubble  backing  and  filling,  usually  varies  from 
about  $8  to  $14  per  cubic  yard. 

Gillette's  "  Handbook  of  Cost  Data  "  gives  a  number  of  detailed 
statements  of  costs  of  stone  masonry.  Such  costs  vary  in  about 
the  same  ratio  as  the  pay  of  labor  employed.  The  unsettled  state 
of  prices  and  labor  costs  since  the  War  make  it  impracticable  to 
give  costs  based  upon  present  prices. 


CHAPTER  IV 
BRICK  AND  BLOCK  MASONRY 

ART.   15.     BUILDING  BRICKS 

56.  Clay  and  Shale  Bricks. — The  cheapness,  ease  of  construction, 
and  durable  qualities  of  good  brick  masonry  make  it  one  of  the  most 
desirable  materials  for  general  structural  work.  It  is  not  as  largely 
used  in  engineering  work  as  stone  or  concrete,  but  in  building  con- 
struction it  is  very  extensively  employed.  The  qualities  of  clay 
bricks  vary  widely  according  to  the  character  of  the  clay  and  methods 
of  manufacture,  and  care  must  be  taken  in  selection  of  material  in 
order  to  secure  good  results. 

Composition  of  Clay  Bricks. — Clay  consists  primarily  of  silicate 
of  alumina.  Common  clays  also  usually  contain  certain  percentages 
of  iron  oxide,  magnesia,  lime,  and  alkalies.  These  are  known  as 
fluxes,  having  the  effect,  when  in  considerable  quantities,  of  making 
the  clay  fusible.  Fire  clays  contain  a  low  percentage  of  fluxes,  and 
withstand  a  high  degree  of  heat  without  fusing. 

Sandy  clays  contain  high  proportions  of  silica  in  an  uncombined 
state,  a  factor  which,  if  not  in  excess,  is  of  value,  tending  to  give 
stability  to  the  form  of  the  brick.  Sand  is  commonly  added  to 
plastic  clays  for  this  purpose. 

The  color  of  the  brick  is  mainly  dependent  upon  the  amount  of 
iron  oxide  present  in  the  clay.  The  color  varies  from  white,  through 
buff  to  red  as  the  percentage  of  iron  oxide  increases.  The  presence 
of  iron  oxide  is  also  of  value  in  adding  strength  and  hardness  to  the 
brick. 

Lime,  when  present  in  appreciable  quantities,  must  be  finely 
divided  and  uniformly  distributed  through  the  clay.  If  in  lumps, 
the  slaking  of  the  lime,  subsequent  to  burning,  may  cause  the  brick 
to  become  distorted  and  cracked.  When  in  excess,  lime  neutralizes 
the  color  effect  of  the  iron  oxide,  making  the  bricks  lighter  in  color, 
buff  or  yellow  colors  being  sometimes  due  to  this  cause. 

Excess  of  alumina  usually  makes  the  clay  very  plastic  and  causes 
it  to  shrink  and  crack  in  drying. 

85 


86  BRICK  AND  BLOCK  MASONRY 

Physical  Properties. — The  physical  properties  of  clay  are  of  more 
importance  than  the  chemical  composition. 

Plasticity  is  one  of  the  important  properties  of  clay  for  brick 
making,  as  it  permits  the  clay  to  be  worked  into  a  plastic  mass,  and 
to  be  molded  into  the  desired  form.  Clay  shrinks  in  drying  and 
also  in  burning,  very  plastic  clay  shrinking  more  than  that  less 
plastic.  Sand  is  frequently  mixed  with  clay  to  reduce  excessive 
shrinkage.  The  degree  of  plasticity  is  sometimes  controlled  by 
mixing  clays  which  differ  in  this  respect. 

When  subjected  to  high  heat,  clay  gradually  becomes  soft  and 
fuses  together,  and  as  the  heat  is  increased  the  softening  and  shrink- 
age progresses  until  the  material  finally  melts  sufficiently  to  lose 
its  shape.  The  temperature  required  for  burning  varies  widely  with 
different  clays,  and  the  degree  of  burning  given  to  brick  depends 
upon  the  kind  of  product  desired  and  the  fusibility  of  the  clay. 

Manufacture. — There  are  three  methods  in  use  for  forming  the 
brick.  They  are  known  as  the  soft-mud,  the  stiff-mud,  and  the  dry- 
press  methods. 

The  soft-mud  process  consists  in  pulverizing  the  clay  or  shale 
and  tempering  it  with  water  to  the  consistency  of  soft  mud.  This 
paste  is  then  pressed  into  wooden  molds,  which  are  usually  sanded 
on  the  surface  to  prevent  the  clay  sticking,  thus  giving  the  brick 
five  sanded  surfaces. 

The  stiff-mud  process  consists  in  mixing  the  pulverized  clay  or 
shale  with  sufficient  water  to  form  a  stiff  paste,  capable  of  retaining 
its  form,  which  is  then  forced  through  a  die,  resulting  in  a  bar  of  the 
section  of  the  brick.  The  bar  is  then  cut  into  bricks  by  wires. 
These  bricks  may  be  either  side  cut  or  end  cut. 

Dry-press  bricks  are  made  by  pressing  pulverized  clay  containing 
a  small  amount  of  moisture  into  steel  molds,  a  method  used  to  secure 
bricks  with  smooth  faces  and  sharp  edges  for  face  brick. 

Repressed  bricks  are  made  by  putting  bricks  made  by  the  soft- 
mud  or  stiff-mud  methods  into  presses  and  subjecting  them  to  high 
pressure.  The  purpose  is  to  give  the  brick  more  perfect  form  and 
sometimes  to  imprint  a  design  upon  the  surface. 

Bricks  made  by  the  wet  method  must  be  dried  before  being  placed 
in  the  kiln.  In  some  yards  this  is  accomplished  by  exposing  the 
molded  bricks  to  the  air  on  floors  or  racks,  while  in  the  larger  plants 
the  drying  is  done  more  rapidly  in  dryers  using  artificial  heat. 

The  burning  is  accomplished  either  in  temporary  kilns,  built 
of  the  brick  to  be  burned,  or  in  permanent  kilns  arranged  usually 
with  fire  boxes  on  the  outside  and  a  downdraft  and  intended  to  give 


BUILDING  BRICKS  87 

uniform  heat  throughout  the  kiln.  This  cannot  be  fully  accomplished 
and  all  of  the  brick  will  not  be  perfectly  burned.  The  degree  of 
burning  received  by  brick  in  temporary  kilns  depends  upon  the 
position  in  the  kiln.  They  must  be  sorted  after  burning  into  various 
shades,  varying  from  the  light  underburned  to  the  dark  arch  brick. 
Good  bricks  may  be  made  by  any  of  the  methods  of  manufacture, 
provided  the  material  is  carefully  handled  and  the  burning  properly 
regulated.  The  differences  due  to  method  used  are  mainly  those 
of  the  form  and  appearance  of  the  brick.  Dry-press  brick  are  usually 
somewhat  softer  and  weaker  than  stiff-mud  brick  of  equally  good 
material. 

CLASSIFICATION  OF  BRICK 

Bricks  used  in  structural  work  may  be  classified  as  follows: 

Common  bricks  are  those  used  for  ordinary  brickwork,  where 
appearance  is  not  of  special  importance.  They  are  burned  at 
moderate  temperatures.  The  best,  well-burned  common  bricks  are 
known  as  hard  or  cherry  bricks,  or  sometimes  as  stock  bricks.  Those 
next  the  fire  and  heavily  burned  are  known  as  clinker  or  arch  bricks. 
Those  from  the  underburned  portion  of  the  kiln  are  known  as  salmon, 
pale  or  soft  bricks.  The  relative  proportions  of  each  kind  in  a  kiln 
vary  with  the  material  and  the  skill  used  in  burning. 

Pressed,  face  or  front  bricks  are  those  made  with  greater  care, 
so  as  to  secure  uniformity  of  form  and  color.  They  are  used  for 
facing  walls  of  common  brick  and  where  appearance  is  important, 
and  are  usually  dry-pressed  or  re-pressed  brick. 

Vitrified  bricks  are  made  from  a  more  refractory  clay  and  burned 
at  a  high  heat  to  the  point  of  vitrification,  so  that  considerable 
softening  and  shrinkage  occurs,  though  the  brick  still  hold  its  shape. 
These  bricks  are  commonly  made  in  larger  sizes  than  common  bricks, 
called  paving  blocks,  and  are  used  in  street  pavements.  They  are 
also  frequently  used  in  building  construction,  where  obtainable  at 
moderate  prices.  Blocks  too  lightly  burned  for  use  in  pavements 
often  make  good  material  for  building  construction. 

Fire  bricks  are  made  from  clay  which  is  lacking  in  fluxing  ingredi- 
ents. They  are  usually  light  in  color,  on  account  of  the  absence  of 
iron  oxide,  and  are  used  when  high  temperatures  are  to  be  resisted. 

Enameled  bricks  are  made  by  coating  the  surface  of  pressed  or 
re-pressed  bricks  before  burning  with  a  slip,  which  will  burn  to  the 
proper  color,  and  covering  with  a  glaze.  The  enamel  is  usually 
applied  to  a  single  surface  of  a  brick. 


88  BRICK  AND  BLOCK  MASONRY 

The  following  designations  are  also  frequently  employed: 

Sewer  bricks  are  those  common  bricks  which  are  so  hard  burned 
as  to  be  practically  non-absorbent  of  moisture,  and  are  commonly 
used  for  lining  sewers. 

Compass  bricks  are  shorter  on  one  edge  than  the  other,  for  use 
in  circular  walls. 

Feather-edge  bricks  are  made  wedge  shaped,  for  use  in  arches. 

Furring  bricks  are  'those  having  a  surface  grooved  for  plastering. 

Ornamental  bricks  are  those  having  designs  stamped  in  relief 
upon  their  faces,  or  bricks  of  special  forms  intended  for  use  in  making 
an  ornamental  surface  design. 

PROPERTIES  OF  CLAY  AND  SHALE  BRICK 

Good  building  brick  should  show  a  uniform  compact  structure 
without  laminations.  They  should  have  plane,  parallel  faces  and 
sharp  edges,  and  should  not  show  kiln  marks  on  their  edges. 

The  dry-pressed  and  re-pressed  bricks  are  usually  smoother  and 
more  accurate  in  shape  than  those  made  by  the  soft-mud  or  stiff- 
mud  processes,  their  density  and  strength  being  largely  dependent 
upon  the  degree  of  burning  and  the  shrinkage  in  the  kiln.  The  under- 
burned,  salmon  bricks  are  porous  and  weak,  and  are  usually  employed 
only  where  strength  is  not  important  and  in  unexposed  positions. 
The  well-burned  cherry  or  hard  bricks  are  the  best  building  brick. 
The  overburned  clinker  bricks  are  more  dense  and  absorb  less  water, 
but  may  be  brittle,  and  are  frequently  distorted  in  shape.  The 
overburned  and  distorted  bricks  ar^  sometimes  used  by  architects 
for  special  exterior  designs  with  very  good  effect. 

Vitrified  bricks,  as  manufactured  for  use  in  paving,  are  superior 
in  strength  and  density  to  common  bricks.  They  frequently  show 
kiln  marks  on  one  side,  due  to  softening  in  the  kiln.  A  clay  for 
making  vitrified  brick  must  burn  at  high  temperatures  and  have 
considerable  range  of  temperature  between  the  point  of  incipient 
fusion  and  the  point  of  vitrification.  It  is  difficult  to  maintain  the 
temperature  uniformly,  so  as  to  burn  a  large  portion  of  the  bricks 
to  the  right  degree,  unless  the  range  of  temperature  is  considerable. 

57.  Sand-lime  Bricks, — Bricks  made  of  sand  cemented  with 
lime  have  been  used  in  a  small  way  for  many  years.  These  bricks, 
as  formerly  made,  were  molded  and  allowed  to  harden  by  standing 
in  the  air,  or  in  an  atmosphere  rich  in  carbon  dioxide  (CO2).  Bricks 
of  this  kind  are  virtually  composed  of  ordinary  lime  mortar,  but 
with  less  lime,  and  are  called  mortar  bricks.  They  depend,  like 


BUILDING   BRICKS  89 

lime  mortar,  upon  the  formation  of  carbonate  of  lime  for  their  harden- 
ing, and  are  weak  and  of  little  value  as  brick,  although  some  struc- 
tures of  such  materials  have  proven  substantial  and  durable. 

In  1881  Dr.  Michaelis  of  Berlin  patented  a  process  of  hardening 
mixtures  of  lime  and  sand  by  the  use  of  steam  at  high  pressure. 
He  discovered  that,  in  the  presence  of  steam  at  high  temperature, 
the  lime  combines  with  a  portion  of  the  silica  of  the  sand,  forming 
a  silicate  of  lime,  which  acts  as  a  cementing  medium.  This  silicate 
is  formed  upon  the  surfaces  of  the  grains  of  sand  and  binds  the 
sand  into  a  single  hard  block. 

About  fifteen  years  after  Michaelis  took  out  his  patent,  the 
manufacture  of  sand-lime  bricks  was  begun  in  Germany  on  a  com- 
mercial scale,  and  soon  developed  into  a  considerable  industry. 
In  1901  the  first  plant  was  opened  in  the  United  States,  and  the 
growth  of  the  industry  in  this  country  was  also  very  rapid. 

Manufacture. — In  the  manufacture  of  sand-lime  bricks,  four 
operations  are  essential: 

(1)  The  lime  must  be  completely  slaked. 

(2)  A  very  uniform  mixture  of  the  lime  and  sand  must  be  obtained. 

(3)  The  material  must  be  formed  into  bricks  under  high  pressure. 

(4)  The  bricks  must  be  subjected  to  the  action  of  steam  at  high 
pressure  for  several  hours. 

The  methods  employed  in  different  plants  for  performing  these 
operations  vary  considerably,  depending  upon  the  character  and 
condition  of  the  materials  employed. 

Hydrated-lime  Process. — In  this  process  the  lime  is  first  slaked 
to  a  powder,  or  a  putty,  and  then  mixed  with  the  sand  and  pressed. 
The  lime  may  be  slaked  by  any  of  the  methods  ordinarily  employed 
in  the  manufacture  of  hydrated  lime,  or  it  may  be  reduced  to  a  paste 
by  the  use  of  an  excess  of  water.  It  is  easier  to  obtain  a  uniform 
mixture  of  the  lime  and  sand  when  dry  hydrated  lime  and  dry  sand 
are  used  and  the  necessary  water  added  afterward.  It  may,  however, 
be  advantageous  sometimes  to  use  wet  materials,  and  good  results 
may  be  obtained  by  either  method  if  the  mixing  be  thorough  and  the 
lime  uniformly  incorporated  in  the  sand. 

Caustic  Lime  Process. — Caustic  lime  is  sometimes  pulverized  and 
mixed  with  the  sand  before  slaking.  Enough  water  is  then  added 
to  slake  the  lime  and  reduce  the  mixture  to  proper  consistency  for 
pressing.  High-calcium  lime,  which  slakes  quickly,  is  necessary 
when  this  method  is  used,  as  sufficient  time  must  be  given  for  the 
complete  slaking  to  take  place  before  the  mixture  goes  to  the  press. 
In  some  plants  the  mixture  is  placed  in  a  silo  and  allowed  to  stand 


90  BRICK   AND  BLOCK  MASONRY 

for  a  few  hours  before  pressing,  in  order  to  insure  that  no  unslaked 
lime  is  left  in  the  mixture  when  the  brick  is  formed. 

The  caustic  lime  process  is  sometimes  modified  by  grinding  the 
lime  with  a  portion  of  the  sand  to  a  fine  powder,  which  is  mixed 
with  the  remainder  of  the  sand,  and  water  added  to  slake  the  lime 
and  wet  the  mixture.  This  is  then  placed  in  a  silo  for  a  sufficient 
period  to  allow  the  lime  to  become  completely  slaked  before  pressing. 
It  is  claimed  that  grinding  the  sand  and  lime  together  produces  an 
intimate  mixture  and  insures  the  complete  combination  during  the 
steaming  into  silicate  which  forms  the  cementing  medium  of  the 
brick.  Grinding  the  lime  and  sand  together  reduces  the  lime  to 
very  fine  condition  and  minimizes  the  danger  from  any  unslaked 
particles  of  lime  left  in  the  mixture,  and  also  fills  the  voids  in  the 
sand  more  completely,  making  a  more  dense  brick. 

Molding. — The  bricks  are  formed  in  molds  similar  to  those 
used  for  dry  clay  bricks,  and  are  subjected  to  high  pressure  in 
molding. 

Hardening. — After  molding,  the  bricks  are  loaded  upon  cars 
and  run  into  the  steaming  cylinders,  where  they  are  subjected  to 
steam  pressure  of  from  100  to  110  pounds  per  square  inch  for  a  period 
of  six  to  ten  hours,  resulting  in  the  combination  of  the  lime  with  the 
silica  into  the  cementing  substance  and  binding  the  sand  into  a 
solid  block.  The  brick  continue  to  harden  and  gain  in  strength  for 
a  time  after  their  removal  from  the  steaming  cylinder,  as  they 
gradually  dry  out. 

Materials. — High-calcium  lime  seems  preferable  for  this  use,  on 
account  of  this  rapid  action  and  the  fine  subdivision  of  its  particles. 
Any  good  lime  may,  however,  be  used  for  the  purpose  if  care  be 
taken  to  insure  that  it  be  completely  slaked. 

The  requirements  for  sand  to  be  used  in  making  sand-lime  bricks 
are  not  essentially  different  from  those  for  sand  to  be  used  in  cement 
mortar.  The  graduation  of  sizes  to  give  a  dense  material  is  desirable. 
The  presence  of  more  fine  material  seems  to  be  needed,  however, 
in  order  to  secure  a  smooth  and  compact  mixture,  and  to  lessen  the 
wear  upon  the  molds,  which  may  become  an  important  item  of  cost. 
Coarse  sands  seem  to  give  stronger  brick,  but  fine  sand  produces 
brick  with  smoother  surfaces. 

Properties  of  Sand-lime  Brick. — In  strength  and  durability,  sand- 
lime  bricks  do  not  differ  materially  from  good  average  clay  bricks. 
When  of  good  quality  they  possess  sufficient  strengths  for  all  the 
purposes  for  which  building  brick  are  ordinarily  employed,  and  are 


BUILDING  BRICKS  91 

usually   more   dense,   and  absorb  less   water    than  common  clay 
bricks. 

Sand-lime  bricks  are  usually  very  uniform  in  size  and  shape,  and 
are  commonly  gray  in  color,  the  shade  depending  upon  the  sand 
used  in  manufacturing  them,  unless  artificially  colored. 

58.  Cement  Bricks. — Bricks  made  of  cement  mortar  or  concrete 
are  used  in  a  number  of  localities.     They  are  commonly  made  of 
mortar,  about  one  part  Portland  cement  to  four  parts  of  sand,  or 
sometimes  of  a  richer  mortar,  1  to  2 J  or  1  to  3,  mixed  with  about 
an  equal  quantity  of  coarser  material,  varying  from  J  to  ^  inch  in 
diameter. 

These  bricks  are  made  by  pressing  in  hand  or  power  presses,  a 
mixture  as  wet  as  is  feasible  to  shape  well  in  the  press.  About  two 
weeks  are  required  for  hardening  before  the  bricks  can  be  used.  The 
materials  need  to  be  carefully  selected,  and  require  the  same  prop- 
erties as  for  mortar  for  use  in  masonry  or  concrete.  The  strength 
may  vary  considerably  with  the  grading  of  the  aggregate,  the  com- 
pression given  to  the  blocks,  and  the  moisture  conditions  under  which 
the  bricks  are  kept  during  the  period  of  hardening,  the  greatest 
strength  will  result  when  they  are  kept  warm  and  thoroughly 
dampened.  The  compressive  strength  at  twenty-eight  days  should 
not  be  less  than  1000  lb./in.2,  and  the  absorption  not  more  than  15 
per  cent. 

Cement  bricks  are  usually  employed  as  face  bricks.  The  appear- 
ance will  depend  upon  the  texture  of  the  aggregates  used  and  the 
method  of  finishing,  which  may  be  smooth  or  roughened  by  the  use 
of  brushes  or  acids.  Color  may  be  given  to  the  bricks  by  the  use 
of  various  mortar  colors. 

59.  Test  for  Building  Brick. — In  determining  the  suitability  of 
a  brick  for  structural  work,  examination  is  commonly  made  of  the 
material  as  to  form  and  texture  with  reference  to  the  particular 
needs  of  the  work  in  hand.     Tests  for  strength  and  absorption  are 
sometimes  included  in  specifications  for  important  work,  but  there 
is  no  recognized  standard  to  which  such  tests  conform,  and  com- 
paratively  little   data  upon  which  to  base  a  reasonable  require- 
ment. 

Form. — For  neat  work,  the  bricks  should  be  uniform  in  size 
with  plane  faces  and  sharp  edges.  Care  in  sorting  is  usually  necessary 
with  clay  brick  to  secure  uniformity  of  color  and  dimension  in  par- 
ticular work. 

Texture. — Good  bricks  should  be  uniform  and  compact  in  struc- 


92 


BRICK  AND  BLOCK  MASONRY 


ture,  should  be  sound  and  free  from  cracks,  and  the  broken  surfaces 
should  be  free  from  flaws  or  lumps.  Clay  brick  should  be  thoroughly 
burned,  and  when  struck  with  a  trowel  or  another  brick  should  give 
a  clear  ringing  sound.  Bricks  which  meet  these  requirements  are 
usually  suitable  for  all  ordinary  work. 

In  ordinary  building  work  little  care  is  usually  given  to  inspec- 
tion of  the  materials,  and  defective  work  frequently  results  from  the 
use  of  poor  bricks.  Seriously  defective  bricks  are  so  easily  detected 
by  inspection  that  there  is  usually  no  excuse  for  their  inclusion  in 
brickwork  of  good  character. 

A  Committee  of  the  American  Society  for  Testing  Materials 
has  been  for  some  time  studying  the  matter  of  a  standard  specifica- 
tion and  standard  tests  for  building  brick.  They  have  suggested 
tentative  methods  for  classification  of  brick  and  for  making  tests 
for  absorption,  compressive  strength,  and  transverse  strength. 

The  committee  recommends  that  the  standard  sizes  for  building 
brick  shall  be  2J  by  3|  by  8  inches. 

They  also  recommend  the  following  classification  of  bricks: 

(a)  According  to  the  results  of  the  physical  tests,  the  bricks  shall  be  classified 
as  vitrified,  hard,  medium,  and  soft  bricks  on  the  basis  of  the  following  require- 
ments: 


Name  of  Grade. 

ABSORPTION  LIMITS, 
PER  CENT. 

COMPRESSIVE  STRENGTH, 
(ON  EDGE) 
LB.  PER  SQ.  IN. 

MODULUS  OF  RUPTURE, 
LB.  PER  SQ.  IN. 

Mean  of 
5  Tests. 

Individual 
Maxi- 
mum. 

Mean  of 
5  Tests. 

Individual 
Mini- 
mum. 

Mean  of 
5  Tests. 

Individual 
Mini- 
mum. 

Vitrified  Brick. 

5  or  less 

6.0 

5000  or  over 

4000 

1200  or  over 

800 

Hard  Brick  

5  to  12 

15.0 

3500  or  over 

2500 

600  or  over 

400 

Medium  Brick  . 

12  to  20 

24.0 

2000  or  over 

1500 

450  or  over 

300 

Soft  Brick  

20  or  over 

No  Limit 

1000  or  over 

800 

300  or  over 

200 

(6)  The  standing  of  any  set  of  bricks  shall  be  determined  by  that  one  of  the 
three  requirements  in  which  it  is  lowest. 


The  methods  proposed  for  making  these  tests  are  given  in  the 
Proceedings  of  the  Society  for  1919,  Part  1,  p.  543. 

Durability  Tests. — The  durability  of  bricks  under  difficult  weather 
conditions  is  one  of  their  most  valuable  qualities.  Tests  are  some- 
times made  of  the  effect  upon  bricks  of  freezing  while  in  a  saturated 


BRICK  MASONRY  93 

condition.  These  tests  have  been  made  in  various  ways,  usually 
by  immersing  the  brick  in  water,  then  freezing  and  thawing  it  repeat- 
edly, commonly  twenty  repetitions,  and  determining  the  loss  of 
weight  or  of  strength.  Very  soft,  porous  bricks  may  be  disinte- 
grated by  such  treatment;  those  of  low  absorption  and  good  strength 
usually  show  but  slight  effect. 

The  Committee  of  the  American  Society  for  Testing  Materials, 
in  1913,  suggested  a  method  for  making  this  test.  They  have  not, 
however,  found  it  of  sufficient  value  to  include  in  their  later  speci- 
fications. 

A  test  in  which  the  brick  is  saturated  with  a  solution  of  sodium 
sulphate,  which  is  then  allowed  to  crystallize  in  the  pores  of  the 
brick,  has  sometimes  been  used,  the  results  of  this  action  being 
similar  to  those  of  freezing,  but  much  more  rapid  and  severe.  A 
study  of  this  method  has  been  made  for  the  Committee  by  Pro- 
fessor Edward  Orton,  Jr.1  and  it  seems  probable  that  it  may  become 
a  standard  method  of  testing  brick.  It  has  not  yet  been  definitely 
formulated  for  use  in  specifications. 


ART.   16.    BRICK  MASONRY 

60.  Joints  in  Brickwork. — In  the  construction  of  brick  masonry, 
it  is  necessary  that  the  joints  between  the  bricks  be  filled  with  mor- 
tar, the  purpose  of  which  is  to  give  a  firm  and  even  bearing  to  the 
bricks,  so  that  the  pressure  upon  them  will  be  uniformly  distributed. 
The  mortar  should  also  adhere  to  the  bricks  and  bind  them  into  a 
monolithic  mass. 

While  thick  joints  usually  make  weaker  masonry  than  those 
that  are  thin,  it  is  desirable  that  the  joint  be  as  thin  as  it  can  readily 
be  made.  When  attempts  are  made  at  too  thin  joints,  they  are 
apt  to  be  imperfectly  filled,  and  thus  weaken  the  masonry.  Joints 
in  wall  masonry  of  common  brick,  as  used  in  building  construction, 
are  usually  from  J  to  f  inch  thick.  It  is  common  to  specify  the 
thickness  of  joints  by  stating  the  thickness  for  eight  courses  of  brick. 
It  is  frequently  required  that  the  thickness  of  eight  courses  of  brick 
masonry  shall  not  exceed  the  thickness  of  eight  courses  of  dry  bricks 
by  more  than  2  inches.  When  pressed  bricks  are  used  for  the  face 
of  a  wall,  the  joints  in  the  face  are  usually  from  J  to  -^  inch  thick. 

1  Proceedings,  American  Society  for  Testing  Materials,  1919,  Part  1. 


94  BRICK  AND  BLOCK  MASONRY 

Pressed  bricks,  being  smoother,  may  be  laid  to  thinner  joints  with 
good  effect.  In  heavy  masonry  as  sometimes  used  in  engineering 
work,  the  joints  usually  of  cement  mortar — are  often  \  inch 
thick. 

Mortar  for  Brickwork. — Lime  mortar  is  more  extensively  used 
for  ordinary  brickwork  in  building  construction  than  any  other. 
Mixtures  of  lime  and  cement  mortars  in  about  equal  quantities  are 
coming  largely  into  use.  The  cement  materially  increases  the 
strength  of  the  mortar  and  its  adhesion  to  the  brick,  while  the 
smoothness  of  the  lime  mortar  is  maintained.  In  important  struc- 
tures, where  considerable  strength  is  needed,  it  is  common  to  use 
cement  .mortar  with  addition  of  10  to  15  per  cent  of  hydrated  lime — 
a  mixture  which  retains  the  strength  of  the  cement  but  makes  the 
mortar  easier  to  work,  and  usually  secures  better  work  than  would 
result  from  the  use  of  cement  alone.  In  engineering  work,  cement 
mortar  is  usually  employed,  but  the  mixture  of  hydrated  lime  with 
the  cement  is  rapidly  coming  into  use. 

Laying  the  Brick. — In  the  construction  of  a  brick  wall  the  two 
outer  courses  are  first  laid,  by  spreading  a  bed  of  mortar  where  the 
brick  is  to  be  placed,  and  against  the  surface  of  the  last  brick  laid, 
then  shoving  the  brick  horizontally  into  place  so  as  to  squeeze  the 
mortar  into  the  bottom  of  the  vertical  joint  between  the  bricks. 
A  bed  of  mortar  is  placed  between  the  outside  bricks  and  the  filling 
bricks  are  shoved  and  pressed  into  place.  Mortar  is  then  slushed 
or  thrown  with  some  force  into  the  upper  part  of  the  vertical  joints 
to  fill  them  completely. 

Bricks  should  be  thoroughly  wet  before  being  laid,  in  order  to 
prevent  the  water  being  absorbed  from  the 
mortar  by  the  brick.  Good  adhesion  cannot 
be  had  between  mortar  and  dry,  porous  bricks. 
In  finishing  joints  upon  the  face  of  the 
wall,  a  flush  joint  may  be  made  by  pressing 
back  the  mortar  with  the  flat  edge  of  the 
trowel.  This  is  usually  done  upon  interior 

walls.      A  weather    joint   may    be    made,    as 
FIG.  33.— Weather  .     ^.      00    ,    J       .  .    ,       £ ' 

Joint  shown  in  Fig.  33,  by  using  the   point   of   the 

trowel  held  obliquely. 

61.  Bond  of  Brickwork. — Brickwork  is  always  laid  in  horizontal 
courses,  and  lateral  bond  is  secured  by  several  different  arrange- 
ments of  the  brick  in  the  courses. 

Common  Bond  is  the  bond  most  commonly  used  in  the  United 


BRICK  MASONRY  95 

States,  for  walls  of  common  brick.  In  this  bond,  one  course  of 
headers  is  used  to  four  to  six  courses  of  stretchers  on  the  face  of  the 
wall,  as  shown  in  Fig.  34. 


1        II        II        II        0        II        II 

I         1         1 

1 

I         II            0 

1            II            1 

II 

I         II            II 

II 

I            II            1 

1 

II      1      II      II      » 

1 

FIG.  34. — Common  Bond. 

In  Flemish  Bond  (Fig.  35),  alternate  headers  and  stretchers  are 
used  in  each  course,  each  header  being  placed  over  the  middle  of  the 
stretcher  in  the  course  below.  Small  closers  are  introduced  next 
to  the  headers  at  the  corners. 


ii    ir 


II  II         II     II         II     II 

II    1  

II  II 

II    II 

II    II 

FIG.  35. — Flemish  Bond. 

English  Bond  consists  of  alternate  layers  of  headers  and  stretchers 
(Fig.  36).  This  construction,  like  the  Flemish  bond,  makes  very 
strong  work.  English  bond  in  which  the  alternate  courses  of 
stretchers  break  joints  with  each  other  is  called  Cross  English  bond. 


96 


BRICK  AND  BLOCK  MASONRY 


Hoop-iron  Bond. — This  consists  in  placing  pieces  of  hoop  iron 
longitudinally  in  the  joints  to  strengthen  the  bond,  the  ends  of  the 
iron  being  turned  down  into  vertical  joints. 

Pressed  Brick  Facing. — In  applying  a  facing  of  pressed  bricks 
to  a  wall  of  common  bricks,  it  is  quite  common  to  lay  all  of  the 
face  bricks  as  stretchers.  When  this  is  done  bond  may  be  obtained 
by  metal  ties  or  by  diagonal  bond. 


1 


J II I 


FIG.  36.— English  Bond. 

Metal  Ties  are  sometimes  used  as  shown  in  Fig.  37.  When  the 
joints  in  the  face  and  backing  cannot  be  brought  to  the  same  level, 
the  metal  tie  may  be  bent,  but  this  is  not  desirable,  and  frequent 
level  joints  should  always  be  possible.  These  ties  may  consist  of 
a  thin  piece  of  galvanized  iron  bent  over  a  wire  at  the  ends,  or  it 
may  be  a  piece  of  galvanized  wire  bent  into  a  loop  at  the  ends  to 
grasp  the  mortar. 


mm/m/////, 


V//////////A 

FIG.  37. — Metal  Ties  for  Face  Brick. 

Diagonal  Bond  consists  in  breaking  off  the  back  corners  of  face 
bricks  and  inserting  bricks  diagonally  to  bond  with  the  face  brick. 

These  bonds  are  not  very  strong,  and  the  face  bricks  are  not  con- 
sidered as  adding  to  the  strength  of  the  wall  or  carrying  any  load. 
Stronger  work  is  obtained  by  using  occasional  courses  of  headers, 


BRICK  MASONRY  97 

or  courses  of  alternate  headers  and  stretchers  as  in  the  Flemish  bond. 
This  is  usually  possible  by  using  care  in  regulating  the  thickness  of 
joints  in  the  backing,  even  when  the  bricks  are  not  of  the  same  sizes. 

Hollow  Brick  Walls. — For  the  purpose  of  providing  air  space 
in  a  wall  to  prevent  the  passing  of  moisture  or  changes  of  temper- 
ature through  it,  hollow  construction  is  sometimes  adopted.  This 
consists  in  building  a  double  wall  with  a  narrow  air  space  between 
the  outer  and  inner  portions. 

It  is  necessary  for  proper  strength  that  the  two  portions  of  the 
wall  be  bonded  in  some  way,  either  by  occasional  headers  which 
span  the  opening  or  by  metal  ties.  The  headers  constitute  a  con- 
nection between  the  masonry  of  the  two  walls,  and  are  sometimes 
objected  to  as  likely  to  cause  moisture  to  pass  from  one  wall  to  the 
other.  The  metal  ties  may  be  provided  with  a  drip  at  the  middle 
which  insures  the  complete  isolation  of  the  walls  from  each  other. 
Such  walls  require  more  careful  work  and  are  more  expensive  to 
construct  than  solid  walls.  When  loads  are  to  be  carried,  one  of  the 
walls  must  be  capable  of  bearing  them. 

62.  Strength  of  Brick  Masonry. — In  tests  which  have  been  made 
on  the  crushing  strength  of  brick  piers,  failure  occurred  by  the  lateral 
bulging  of  the  piers.  When  pressure  is  applied  longitudinally  upon 
the  pier,  a  lateral  expansion  normal  to  the  direction  of  pressure 
results.  This  causes  tension  upon  the  brickwork  and  the  pier  yields 
through  breaking  the  bricks  in  tension  and  pulling  apart  of  joints. 
The  transverse  strength  of  the  bricks  may  also  be  called  into  play 
when  they  are  not  bedded  with  perfect  evenness — a  fact  proven  by 
a  series  of  tests  on  brick  piers  at  the  Watertown  arsenal  in  1907, 
in  which  bricks  set  on  edge  gave  somewhat  higher  strengths  than 
when  laid  flat.  Piers  in  which  the  joints  were  broken  at  every  third 
or  sixth  course  gave  slightly  better  results  than  those  breaking 
joints  at  every  course,  as  was  also  observed  in  piers  tested  in  1884. 

The  strength  of  brickwork  depends  upon  the  bond  as  well  as 
upon  the  adhesion  of  the  mortar  and  the  strength  of  the  bricks. 
In  masonry  to  be  subjected  to  heavy  loads,  careful  attention  should 
be  given  to  the  bonding  of  the  work  and  to  the  complete  filling  of 
the  vertical  joints  in  laying  the  masonry. 

The  advantage  of  using  strong  mortar  in  such  work  is  demon- 
strated by  many  tests  made  at  Watertown  arsenal  and  reported  by 
the  Ordnance  Department  of  the  United  States  Army  in  "  Tests  of 
Metals,  etc."  That  the  strength  of  brick  masonry  in  piers  is  some- 
what proportional  to  the  strength  of  the  bricks  is  also  demonstrated 
by  these  tests. 


98 


BRICK  AND  BLOCK  MASONRY 


A  series  of  tests  made  by  A.  N.  Talbot  and  D.  A.  Abrams  at  the 
University  of  Illinois  Experiment  Station  in  1908  gives  very  inter- 
esting results.  A  summary  of  these  results  is  given  in  Table  VI. 

TABLE  VI 

SUMMARY  OF  TESTS  OF  BRICK  COLUMN 
Average  Values 


Ratio  of 

Ratio  of 

Crushing 

Ratio  of 

Ref. 

Characteristics  of  Columns. 

Average 
Unit 
Load,  Ib. 

Strength 
of  Column 
to 

Strength 
of  Column 
to 

Strength 
of  6-in. 
Mortar 

Strength 
of  Column 
to 

per  sq.  in. 

Strength 
of  Brick 

Strength 
of  "A" 

Cubes,  Ib. 
per  sq.  in. 

Strength 
of  Cubes 

Shale  Building  Brick 


A 

Well    laid,    1:3  Portland 

cement  mortar,  67  days. 

3365 

.31 

1.00 

2870* 

1.17 

B 

Well    laid,    1:3  Portland 

cement  mortar,  6  months 

3950 

.37 

1.18 

.... 

.... 

C 

WeU   laid,    1:3  Portland 

cement   mortar,    eccen- 

trically loaded,  68  days. 

2800 

.26 

.83 

.... 

.... 

D 

Poorly  laid,  1  :  3  Portland 

cement  mortar,  67  days. 

2920 

.27 

.87 

2870* 

1.05 

E 

Well    laid,    1:5  Portland 

cement  mortar,  65  days. 

2225 

.21 

.66 

1710 

1.30 

F 

Well    laid,     1:3    natural 

cement  mortar,  67  days. 

1750 

.16 

.52 

305 

5.75 

G 

Well  laid,  1  :  2  lime  mortar, 

66  days       

1450 

.14 

.43 

Underburned  Clay  Brick 


H 

Well    laid,   1:3    Portland 
cement  mortar,  63  days. 

1060 

.27 

.31 

2870* 

.37 

*  Average  value  based  on  1  : 3  tests  of  1 : 3  Portland  cement  mortar  cubes  sixty  days  old. 

In  the  testing  of  brick  piers  it  has  been  found  that  the  initial 
yielding  of  the  pier  usually  occurs  at  about  one-half  the  breaking 
load.  The  safe  load  should  be  taken  at  not  more  than  one-tenth 
to  one-twelfth  of  the  breaking  load,  on  account  of  the  many  elements 
of  uncertainty  concerning  the  actual  strength,  chances  for  defective 
work,  etc. 


BRICK  MASONRY 


99 


A  committee  of  engineers  and  architects  recommended  to  the 
City  of  Chicago  in  1908,  the  following  values  to  be  used  as  safe 
working  pressures  for  brick  masonry  in  building  construction: 


Common  Brick  of  Crushing  Strength 
Equal  to  1800  lb./in.2 

Lb.  per 

Sq.  In. 

Tons  per 
Sq.  Ft. 

In  Iiin6  mortar 

100 

7   2 

In  lime  and  cement  mortar  

125 

9.0 

In  natural-cement  mortar            

150 

10  8 

In  Portland-cement  mortar  

175 

12.6 

Select,  Hard,  Common  Brick,  of  Crushing  Strength  Equal 
to  2500  Lb  per  Sq.  In. 

In  1  part  Portland  cement,  1  lime  paste  and  3  sand 
In  1  *  3  Portland  cement  mortar 

175 

200 

12.6 
14  4 

Pressed  and   Sewer-brick,   of  Crushing  Strength  Equal  to 
5000  Lb.  per  Sq.  In. 

In  1  :  3  Portland  cement  mortar  
Paving  brick,  in  1  :  3  Portland  cement  mortar  

250 
350 

18.0 
25.2 

The  building  code  of  the  City  of  St.  Louis,  in  1917,  gives  the 
following  allowable  compression  on  brick  masonry: 


Vitrified  paving  brick,  one  part  Portland  cement,  three  parts  sand . . 
Strictly  hard  pressed  brick,  one  part  Portland  cement,  three  parts 

sand 

Ordinary  hard  and  red  brick,  one  part  Portland  cement,  three  parts 

sand 

Ordinary  hard  and  red  brick,  one  part  Portland  cement,  one  lime, 

three  sand 

Merchantable  brick,  good  lime  mortar 


Per  sq.  in. 

300 
250 
200 

175 
100 


Vitrified  paving  brick  and  strictly  hard  brick  shall  not  crush  at  less  than 
five  thousand  (5000)  pounds  pressure  per  square  inch.  Ordinary  hard  and  red 
brick  shall  not  crush  at  less  than  two  thousand  and  three  hundred  (2300)  pounds 
pressure  per  square  inch.  Merchantable  brick  shall  not  crush  at  less  than  one 
thousand  and  eight  hundred  (1800)  pounds  pressure  per  square  inch. 

63.  Efflorescence. — The  appearance  of  brick  masonry  is  sometimes 
marred  by  a  white  coating  which  exudes  from  the  masonry  and  is 
deposited  upon  its  surface.  This  is  called  efflorescence,  and  is  caused 
by  soluble  salts  in  the  brick  or  the  mortar,  usually  the  latter,  which 


100  BRICK  AND  BLOCK  MASONRY 

are  dissolved  by  water  when  the  wall  is  wet  and  deposited  on  the 
surface  as  the  water  evaporates.  Such  deposits  usually  consist  of 
salts  of  soda,  potash,  or  magnesia  contained  in  the  lime  or  cement, 
or  of  sulphate  of  lime  or  magnesia  from  the  brick. 

Efflorescence  may  be  prevented  by  keeping  the  wall  dry.  The 
use  of  impervious  materials,  and  making  the  masonry  itself  imperme- 
able, render  the  appearance  of  efflorescence  improbable.  When  a 
wall  is  in  a  damp  situation,  a  damp-proof  course  at  the  base  of  the 
wall  to  prevent  moisture  rising  in  the  masonry  is  desirable.  If  the 
masonry  is  permeable  and  is  dampened  by  rain,  some  waterproof 
coating  may  be  applied  to  the  surface  of  the  wall.  There  are  various 
patented  preparations  for  this  purpose,  and  the  Sylvester  process 
is  sometimes  successfully  used.  This  consists  in  applying  first  a 
wash  of  aluminum  sulphate  (1  pound  to  1  gallon  of  water),  and  then 
a  soap  solution  (2.2  pounds  of  hard  soap  per  gallon  of  water).  These 
applications  are  made  twenty-four  hours  apart.  The  soap  solution 
is  applied  at  boiling  temperature.  The  walls  must  be  dry  and  clean, 
and  the  air  temperature  should  not  be  below  about  50°  F.  when 
the  application  is  made. 

Efflorescence  may  usually  be  removed  by  scrubbing  with  a  weak 
solution  of  hydrochloric  acid. 

64.  Measurement  and  Cost. — Measurement  of  brickwork  is 
usually  made  by  estimating  the  number  of  thousand  bricks.  It 
is  assumed  that  an  8-  or  9-inch  wall  contains  15  bricks  per  square 
foot  of  surface;  a  13-inch  wall,  22 \  bricks;  a  17-  or  18-inch  wall, 
30  bricks,  etc.  These  numbers  are  employed  without  regard  to  the 
actual  size  of  the  bricks,  adjustments  in  price  per  thousand  being 
made  for  various  sizes. 

The  methods  of  estimating  are  sometimes  rather  complicated 
and  are  subject  to  rules  established  by  custom.  The  plain  wall  is 
the  standard  of  measurement,  openings  less  than  80  square  feet  are 
usually  not  deducted;  larger  openings  are  measured  2  feet  less  in 
width  than  they  actually  are.  Hollow  walls  and  chimneys  are 
measured  solid. 

A  pier  is  sometimes  measured  as  a  wall  whose  length  is  the  cir- 
cumference and  whose  thickness  is  the  width  of  the  pier.  Some- 
times one-half  the  circumference  is  taken  as  the  length. 

Stone  trimmings  are  not  deducted  from  the  brickwork  measure- 
ments. Various  rather  complicated  rules  are  used  in  estimating 
footings,  pilasters,  detached  chimneys,  etc. 

Having  estimated  the  work  in  thousands  of  brick  by  these  rules, 
a  price  per  thousand,  suited  to  the  plain  wall,  is  used  for  the  entire 


BRICK  MvlASGNBtfi  £  ^  i  ;  /,  101 

job.  When  pressed  brick  facing  is  used,  the  area  of  such  facing  is 
separately  estimated.  If  an  ashlar  facing  be  used,  its  thickness 
is  not  included  in  that  of  the  brick  wall. 

In  engineering  work,  brickwork  is  usually  measured,  like  stone 
masonry,  by  the  cubic  yard  of  actual  masonry. 

Number  of  Bricks  Required. — The  actual  number  of  bricks 
needed  for  the  construction  of  masonry  varies  with  the  size  of  the 
bricks  and  the  thickness  of  joints.  For  ordinary  brickwork,  with 
common  bricks  of  the  usual  (8iX4X2J  inches)  size,  and  joints  J  to 
f  inch  thick,  1000  bricks  will  lay  about  2  cubic  yards  of  masonry.  If 
the  joints  be  J  to  f  inch  thick,  1000  bricks  will  lay  about  2|  cubic 
yards. 

With  common  bricks  of  ordinary  size  in  masonry  walls,  six  bricks 
will  usually  be  required  per  square  foot  of  wall  surface  for  each  width 
of  brick  in  the  thickness  of  the  wall.  For  ordinary  pressed-brick 
fronts,  6  to  6^  bricks  are  required  per  square  foot  of  actual  wall  sur- 
face. In  average  building  construction,  deductions  for  openings 
will  reduce  the  number  by  about  one-third  of  those  required  for 
solid  wall. 

Mortar  Required. — For  ordinary  building  construction  with  J  to 
f-inch  joints,  0.5  to  0.6  cubic  yard  of  mortar  is  required  per  1000 
bricks.  This  needs  for  1  to  3  portland  cement  mortar,  about  1.5 
barrels  of  cement  and  0.6  cubic  yard  of  sand;  for  lime  mortar 
about  200  pounds  (2J  bushels)  of  lime  and  0.6  cubic  yard  of  sand. 

In  heavy  masonry  with  joints  \  to  f  inch,  about  0.35  to  0.40 
cubic  yard  of  mortar  per  cubic  yard  of  masonry,  or  approximately 
one  barrel  of  cement  and  0.4  cubic  yard  of  sand  for  1  to  3  Portland 
cement  mortar. 

Labor  of  Laying  Bricks. — A  bricklayer  on  ordinary  work  may 
lay  from  about  125  to  175  common  bricks  per  hour,  according  to 
the  skill  of  the  workman  and  the  organization  of  the  work.  He 
should  place  somewhat  less  than  half  as  many  face  bricks.  The 
number  of  bricks  laid  may  be  somewhat  less  with  cement  mortar 
than  with  lime  mortar.  On  thin  walls,  with  careful  work,  one  helper 
may  be  needed  for  two  bricklayers.  On  common  brickwork,  in 
building  construction,  one  helper  may  be  needed  for  each  mason. 

In  recent  work  with  masons  at  60  to  70  cents  per  hour,  helpers 
at  30  to  35  cents  per  hour,  lime  at  40  to  50  cents  per  bushel,  the  cost 
of  laying  common  bricks  in  the  walls  of  buildings  has  run  from  $5 
to  $8  per  1000  bricks.  Costs  for  scaffolding,  for  machinery  and 
labor  in  erection  of  brickwork  necessarily  vary  materially  with  the 
conditions  under  which  the  work  must  be  done. 


102  BRICK;  ANfe  BLG.CK  .MASONRY 

At  prices  which  have  existed  since  the  World  War,  these  figures 
would  be  largely  increased.  Costs  have  varied  widely  in  different 
localities  and  are  now  very  unstable. 


ART.   17.    TERRA  COTTA  CONSTRUCTION 

65.  Structural  Tiling.— Hollow  tiling  for  use  in  building  con- 
struction is  made  in  many  different  forms.  It  is  employed  either 
as  the  main  structural  material  or  as  fireproof  covering  for  other 
materials. 

The  materials  of  which  the  tiles  are  made  are  similar  to  those 
used  in  making  bricks,  but  requiring  usually  higher  grade  and  more 
refractory  materials.  Shales  or  semi-fire  clays,  similar  to  those  used 
for  paving  bricks,  are  frequently  employed  for  this  purpose,  or  some- 
times fire  clays  are  mixed  with  plastic  clays  to  prevent  fluxing  at 
moderate  temperatures.  Tiling  for  use  in  construction  may  be 
made  either  dense  or  porous  according  to  the  qualities  desired. 

Dense  Tiling  is  made  from  materials  which  vitrify  at  high  tem- 
peratures (above  2000°  F.)  and  is  burned  to  the  point  of  vitrifica- 
tion like  paving  bricks.  This  material  when  of  good  quality  pos- 
sesses high  strength  and  is  practically  non-absorbent.  It  is  used 
in  outer  walls  of  buildings,  or  for  floor  and  wall  construction  when 
strength  is  needed. 

Hollow  blocks  as  made  for  ordinary  wall  construction  are  not 
usually  vitrified,  but  are  burned  to  a  less  degree  than  the  best  dense 
tiling.  They  must  be  hard  burned  to  be  of  value.  In  the  rapid 
growth  of  the  tile  industry,  attempts  have  been  made  to  produce 
hollow  tiling  from  inferior  materials,  and  soft  tiles  lacking  in  strength 
and  durability  have  sometimes  been  offered.  Care  must  be  exercised 
in  selecting  tiling  to  make  sure  of  its  quality. 

Porous  Tiling,  or  Terra  Cotta  Lumber,  is  made  from  refractory 
plastic  clays  by  mixing  sawdust  with  the  clay  in  forming  the  blocks, 
and  burning  at  high  temperature.  The  sawdust  burning  out  leaves 
the  material  light  in  weight  and  porous.  These  blocks  may  be  cut 
with,  a  saw,  and  nails  or  screws  may  be  driven  into  them  without 
difficulty.  This  tiling  does  not  possess  the  strength  of  good  dense 
tiling,  but  is  tough  and  less  brittle,  and  is  largely  used  in  fireproofing 
and  for  interior  walls  and  partitions. 

Tiling  of  less  porosity  but  possessing  somewhat  the  character  of 
th6  terra  cotta  lumber  is  sometimes  made  by  mixing  ground  coal 
with  the  clay  before  burning.  It  is  claimed  that  this  makes  a  better 


TERRA  COTTA  CONSTRUCTION 


103 


fireproofing  than  the  dense  tiling.  These  blocks  are  sometimes 
known  as  semi-porous  tiling. 

The  forms  and  sizes  of  hollow  blocks  depend  upon  the  uses  to 
be  made  of  them.  For  walls  or  partitions,  the  blocks  are  usually 
in  12-inch  lengths,  and  of  rectangular  or  interlocking  sections. 

Rectangular  blocks  are  made  in  various  sizes — 12-inch  widths 
may  be  had  from  2  inches  to  8  inches  thick.  Widths  of  6  and  8 
inches  are  made  in  thicknesses  from  2  to  5  inches.  They  are  divided 
by  webs  into  cells,  as  shown  in  Fig.  38.  In  the  heavier  tiling,  intended 


Fro.  38.— Hollow  Rectangular  Blocks. 

for  use  where  loads  are  to  be  carried,  and  in  outside  walls,  the  shells 
are  at  least  1  inch  and  the  webs  at  least  f-inch  in  thickness,  and  the 
cells  not  more  than  3J  or  4  inches  in  width.  In  lighter  tiling,  used 
as  filler  in  concrete  work  or  for  light  partitions,  the  webs  are  f  to  J 
inch,  and  cell  openings  may  be  5  or  6  inches. 

Interlocking  blocks  are  made  in  various  shapes,  with  the  object 
of  improving  the  bond  of  the  wall,  and  eliminating  joints  extending 
through  the  wall.  These  blocks  are  often  used  in  outside  walls  to 
prevent  moisture  passing  through  the  wall  and  provide  air  spaces 
in  all  parts  of  the  wall.  Fig.  39  shows  one  of  the  common  forms 
of  interlocking  tile. 

Hollow  blocks  for  use  in  fire  protection  are  made  in  many  shapes 
to  fit  around  structural  members  of  other  materials.  They  are  also 
made  to  fit  together  in  round  or  flat  arches  to  support  floors  between 
steel  beams. 


104 


BRICK  AND  BLOCK  MASONRY 


Good  tiling  must  be  well  burned,  true  in  form  and  free  from  checks 
or  cracks,  and  should  give  a  ringing  sound  when  struck  with  metal. 

The  following  requirements  for  hollow  tile  are  given  in  the  Build- 
ing Code  of  the  city  of  St.  Louis  for  1917: 

All  hollow  tile  used  in  the  construction  of  walls  or  partitions  shall  be  hollow 
shale  or  terra  cotta,  well  manufactured  and  free  from  checks  and  cracks,  each 
piece  or  block  to  be  molded  square  and  true  and  to  be  hard  burned  so  as  to  give 
a  good  clear  ring  when  struck,  and  not  to  absorb  more  than  twelve  (12)  per  cent 
of  its  own  weight  in  moisture.  Each  of  said  blocks  shall  develop  an  ultimate 
crushing  strength  of  not  less  than  three  thousand  (3000)  pounds  per  square  inch 
of  available  section  of  web  area,  and  shall  not  be  loaded  when  in  the  wall  more 
than  eighty  (80)  pounds  per  square  inch  of  effective  bearing  area.  Tiles  shall 


FIG.  39. — Interlocking  Tile. 

have  outer  shells  or  walls  not  less  than  three-quarters  (f)  of  an  inch  thick  and 
shall  be  additionally  reinforced  by  continuous  interior  walls  or  webs  which  shall 
not  be  less  than  one-half  (^)  inch  thick,  and  so  arranged  that  no  void  shall  exceed 
four  (4)  inches  in  cross-section  at  any  point.  It  is  further  provided  that  the 
building  commissioner  may  require  a  test  to  be  made  of  such  blocks  before  allow- 
ing the  same  to  be  placed  in  the  wall,  if,  in  his  judgment,  there  be  any  doubt 
as  to  whether  such  blocks,  proposed  to  be  used,  meet  the  requirements  above 
specified. 

66.  Block  Construction. — In  the  construction  of  walls  of  ordi- 
nary hollow  rectangular  blocks,  the  blocks  are  usually  laid  so  as  to 
break  joints  and  extend  through  the  walls.  They  should  be  so 
placed  that  the  vertical  webs  in  each  course  are  directly  above  those 
in  the  course  below.  Such  construction  is  shown  in  Fig.  38. 

In  using  tile  with  horizontal  cells,  jamb  blocks  and  corner  blocks 
are  made  with  the  cells  vertical.  When  very  light  walls  are  used, 
longitudinal  reinforcement,  consisting  of  thin  band  iron  or  of  special 
forms  of  wire  mesh,  is  placed  in  the  joints.  This  is  necessary  for 
2-inch  partitions  or  for  3-inch  partitions  more  than  10  feet  high. 


TERRA  GOTTA  CONSTRUCTION 


105 


Tiles  with  vertical  cell  openings  are  made  by  some  makers.    Fig. 
40  shows  construction  with  standard  tiling  of  this  type. 


FIG.  40. — Walls  of  Natco  Hollow  Blocks. 

Portland  cement  mortar,  or  mortar  of  lime  and  cement,  is  used 
in  laying  hollow  blocks.  In  walls  which  are  to  carry  considerable 
loads,  Portland  cement  with  10  to  15  per  cent  of  hydrated  lime  by 
volume  (4  to  6  per  cent  by  weight)  should  be  used  in  1  to  3  mortar 
with  well-graded  sand.  For  walls  which  are  not  to  carry  loads,  a 
larger  amount  (equal  volumes)  of  lime  may  be  used.  The  surfaces 
of  tiles  are  often  grooved  to  aid  the  adhesion  of  the  mortar  in  the 
joints.  When  the  finish  of  the  wall  is  to  be  plaster  or  stucco,  the 
surface  of  the  tile  is  grooved  to  hold  the  plaster.  If  brick  veneer  is 
to  be  applied,  or  if  the  surface  of  the  tile  is  to  be  used  for  exterior 
finish,  a  smooth  finish  may  be  desirable. 

Floor  Construction. — The  method  of  using  hollow  blocks  in  flat 
arch  floor  construction  is  shown  in  Fig.  41.  These  arches  vary  from 


FIG.  41. — Flat  Arch  Floor  Construction. 

about  3  to  6  feet  in  span  and  from  6  to  12  inches  in  depth.     The 
blocks  required  consist  of  the  skewback,  the  fillers  and  the  key-block. 


106 


BRICK  AND  BLOCK  MASONRY 


The  skewbacks  are  usually  made  of  such  form  as  to  enclose  the 
bottom  of  the  I-beam  for  fire  protection. 

Such  arches  are  now  commonly  made  by  the  end-construction 
method  in  which  the  cell  openings  run  lengthwise  of  the  arch.  The 
blocks  do  not  break  joints,  but  form  a  series  of  independent  arches 
side  by  side.  A  number  of  different  shapes  are  offered  for  these 
arches  by  different  makers,  lighter  weight  being  obtained  than  with 
side-construction  arches  for  the  same  strength. 

Hollow  blocks  are  frequently  used  as  fillers  in  reinforced  con- 
crete floors,  the  blocks  filling  spaces  between  the  webs  of  the  T-beams 
of  concrete,  as  shown  in  Fig.  42.  Blocks  12  inches  wide  are  usually 


FIG.  42.— Hollow  Block  Fillers  in  Concrete  Floors. 

employed  for  this  purpose,  the  depth  depending  upon  the  span  and 
loading  of  the  floor. 

Strength  of  Block  Masonry. — Comparatively  few  data  are  avail- 
able upon  the  strength  of  constructions  of  terra-cotta  blocks.  A 
very  carefully  constructed  wall  of  natco  tile  (see  Fig.  40)  was  tested 
by  R.  W.  Hunt  &  Company.  The  wall  was  36f  inches  long,  8  inches 
thick,  and  12  feet  2\  inches  high,  and  was  twenty-eight  days  old 
when  tested.  It  failed  under  a  load  of  436,000  pounds,  giving  a 
compression  of  3110  lb./in.2  on  the  net  section  of  the  web,  or  about 
1500  lb./in.2  of  gross  area.  Tests  of  a  wall  of  Denison  tile  (see  Fig. 
39)  faced  with  brick,  forty-two  days  old,  was  made  at  the  labo- 
ratory of  the  Bureau  of  Standards.  This  wall  was  5  feet,  1  inch  in 
length,  12J  inches  thick,  and  31  feet  high.  It  carried  a  load  of 
686,000  pounds,  or  about  900  lb./in.2  of  gross  area. 

Good  dense  tiling  should  have  a  crushing  strength  of  3000  to 
6000  lb./in.2  of  net  section.  When  laid  in  masonry  the  allowable 
load  is  usually  not  more  than  one-fifteenth  of  the  ultimate  strength 
of  the  block.  Carefully  laid  masonry  of  good  quality  hollow  blocks 
may  be  allowed  to  carry  a  load  of  200  lb./in.2  of  net  section  of  block, 
or  in  general  about  5  tons  per  square  foot  of  gross  area. 

67.  Architectural  Terra-cotta. — Terra-cotta  for  exterior  finish  or 
ornamental  work  is  usually  made  from  a  mixture  of  clays,  carefully 
selected  to  secure  the  desired  qualities.  The  clay  is  ground,  mixed, 
tempered,  and  worked  to  a  proper  condition  of  plasticity.  It  is 


GYPSUM  AND  CEMENT  CONCRETE  BLOCKS  107 

then  formed  into  the  desired  shapes  in  plaster  molds  or  by  hand, 
modeled  as  may  be  necessary,  and  dried.  After  drying,  it  is  given 
a  surface  treatment,  by  spraying  with  a  liquid  upon  the  surface, 
which  determines  the  kind  of  finish  to  be  given  in  burning  and  its 
color. 

The  blocks  of  terra-cotta  may  have  a  length  up  to  30  inches,  and 
depth  of  6  to  10  inches,  with  height  according  to  the  requirements 
of  the  work.  They  are  constructed  as  hollow  shells  with  webs  about 
1J  inches  thick,  and  cells  6  inches  or  less  in  width.  These  blocks 
are  built  into  the  body  of  the  wall  by  bonding  the  masonry  into  and 
filling  the  cells. 

Several  kinds  of  surface  finish  are  used  for  terra-cotta.  Standard 
terra-cotta  is  that  in  which  no  special  finish  is  applied,  leaving  the 
block  somewhat  porous.  Vitreous  terra-cotta  has  a  spray  applied  to 
the  surface  which  causes  the  surface  material  to  vitrify  during  burn- 
ing, making  the  material  non-absorbent.  Glazed  terra-cotta  has  an 
impervious  coating  of  glaze  upon  the  surface.  When  the  glaze  is 
deadened,  it  is  called  mat-glazed.  A  variety  of  colors  are  available 
for  use  with  this  material,  and  make  its  use  possible  in  a  wide  range 
of  artistic  designs. 

Terra-cotta  of  good  quality  is  one  of  the  most  durable  materials 
for  use  in  the  trimming  and  ornamentation  of  masonry  structures. 
Being  practically  non-absorbent,  it  is  not  affected  by  frost,  or  by 
the  gases  in  the  atmosphere.  The  facility  with  which  it  may  be 
worked  into  desired  forms  makes  it  a  desirable  material  for  artistic 
design. 


ART.  18.    GYPSUM  AND  CEMENT  BLOCK  CONCRETE 

68.  Gypsum  Wall  Blocks. — Blocks  made  by  mixing  gypsum 
plaster  (see  Section  37)  with  wood  fiber  or  similar  materials  are  used 
for  partition  walls  in  fireproof  building  construction.  They  are  made 
30  inches  long,  12  inches  high,  and  from  3  to  8  inches  thick,  with 
tapering  openings  through  the  block. 

They  are  laid  in  the  wall  to  break  joints  and  cemented  with 
mortar  composed  of  gypsum  cement  plaster  and  sand,  usually  1  to 
3.  They  are  not  used  for  walls  bearing  loads,  but  form  very  light 
partitions,  and  have  good  soundproof  and  fireproof  qualities. 

The  3-inch  blocks  are  used  to  a  height  of  wall  of  about  12  feet, 
the  4-inch  to  17  feet,  and  the  6-inch  to  24  feet.  The  material  may 
be  cut  with  a  saw,  and  plaster  is  applied  directly  to  their  surfaces. 


108  BRICK  AND  BLOCK  MASONRY 

The  weights  of  walls  of  hollow  gypsum  blocks  are  approximately 
as  follows : 

Thickness  of  block,  inches 3      4      5      6      8 

Weight  of  wall,lb  per  sq.  ft 10     13     16    20    26 

Three  pounds  per  square  foot  is  added  for  plaster  upon  each  side 
of  the  wall. 

69.  Roofing  and  Floor  Blocks. — Blocks  of  gypsum,  similar  in 
composition  to  the  partition  blocks,  and  reinforced  with  wire  mesh, 
are  made  both  in  solid  and  hollow  form  for  use  in  roof  construction. 
They  are  usually  3  or  4  feet  in  length  and  are  used  to  span  the  open- 
ings between  purlins  and  form  a  solid  deck  upon  which  the  roof 
covering  may  be  placed.  They  are  made  with  beveled  edges,  and 
are  set  with  their  lower  edges  in  contact  and  the  triangular  openings 
between  them  filled  with  a  grout  of  cement  plaster.  Blocks  with 
heavier  reinforcement  for  openings  up  to  10  feet  in  span  are  also 
now  offered. 

Floor  blocks,  to  be  used  as  fillers  in  reinforced-concrete  floor  con- 
struction, are  now  available.  These  are  designed  to  act  as  forms 
for  the  concrete,  and  require  support  at  the  ends  of  the  blocks,  which 
are  2  feet  long.  A  spacer  is  placed  between  two  adjoining  blocks  to 
hold  the  concrete  for  the  web  of  the  beam,  forming  a  smooth  surface 
on  the  under  side  upon  which  plaster  may  be  placed.  A  section  of 
floor  constructed  with  these  blocks  is  shown  in  Fig.  43. 


FIG.  43. — Pyrobar  Gypsum  Floor  Tile. 

70.  Concrete  Blocks. — Hollow  building  blocks  of  Portland  cement 
concrete  are  frequently  employed  in  building  construction  in  the 
same  manner  as  in  solid  concrete  construction,  given  in  Chapter  V, 
and  the  concrete  is  proportioned  and  mixed  in  the  same  manner. 

The  blocks  are  usually  made  to  set  in  the  wall  with  the  webs  in 
a  vertical  position.  Several  patented  forms  are  on  the  market 
which  make  blocks  to  bond  in  the  wall  in  different  ways  and  giving 
air  spaces  more  or  less  effective  as  insulation  against  moisture  and 
heat.  Such  blocks,  when  well  made  and  properly  set,  make  a  sub- 


GYPSUM  AND  CEMENT  CONCRETE  BLOCKS  109 

stantial  and  durable  building,  and  may  be  used  in  such  manner  as 
to  give  a  pleasing  appearance.  The  color  of  the  blocks  may  be 
regulated  by  choice  of  the  aggregate  used  upon  their  exposed  faces. 
The  use  of  coloring  matter  in  the  concrete  has  not  usually  been  very 
successful,  although  there  are  mineral  colors  available  which  may 
be  used  without  material  injury  to  the  concrete. 

Metal  molds  are  commonly  employed,  and  concrete  of  rather 
dry  consistency  is  compressed  into  them  by  tamping  or  by  hydraulic 
pressure.  This  yields  concrete  of  greatest  strength  and  also  makes 
a  block  which  may  be  quickly  removed  from  the  mold.  For  orna- 
mental work,  sand  molds  are  frequently  employed,  a  wooden  pattern 
being  used  in  forming  the  mold,  and  the  concrete  poured  in  a  wet 
mixture. 

The  curing  of  the  blocks  is  important  in  its  effect  upon  the 
strength  and  durability  of  the  concrete,  which  must  not  dry  out 
during  the  period  of  hardening.  After  the  blocks  are  removed  from 
the  molds,  they  are  allowed  to  stand  in  the  air  until  the  cement  has 
set,  when  they  may  be  transferred  to  a  steam  chamber,  where  they 
are  subjected  to  an  atmosphere  charged  with  steam  at  a  temperature 
about  110°  to  130°  F.  After  two  or  three  days  in  the  steam,  they 
may  be  removed  to  the  open  air,  but  should  be  sprinkled  often 
enough  to  keep  them  continually  damp  for  ten  or  twelve  days.  When 
a  steam  chamber  is  not  employed,  the  blocks  are  cured  in  the  open 
air,  but  should  be  kept  wet  for  a  longer  period  to  give  time  for  com- 
plete hardening.  The  temperature  to  which  they  are  subjected 
during  hardening  should  never  go  lower  than  about  50°  F. 


CHAPTER  V 
PLAIN  CONCRETE 

ART.   19.  AGGREGATES  FOR   CONCRETE 

71.  Materials  Used  for  Aggregates. — Concrete  as  used  in  con- 
struction is  essentially  a  mixture  of  cement  mortar  with  broken 
stone,  gravel,  or  other  coarse  material.  The  mortar  serves  to  fill 
the  voids  in  the  stone  and  the  whole  is  bound  into  a  solid  monolith 
by  the  setting  and  hardening  of  the  cement. 

The  materials  mixed  with  the  cement  in  forming  concretes  are 
known  as  aggregates.  The  sand  or  stone  chips  in  the  mortar  is 
called  the  fine  aggregate  and  the  coarser  gravel  or  broken  stone  is 
the  coarse  aggregate.  In  the  manufacture  of  good  concrete  it  is 
essential  that  each  of  the  materials  be  of  proper  quality,  and  that 
they  be  properly  proportioned  and  incorporated  into  the  mixture. 

Fine  Aggregate. — Material  which  will  pass  a  J-inch  screen  is 
usually  included  under  the  term  fine  aggregate,  or  sand.  The 
requirements  for  sand  and  its  use  in  mortar  have  been  discussed  in 
Chapter  II.  Ordinarily,  the  sand  which  makes  the  strongest  and 
most  dense  mortar  will  also  give  the  best  results  in  concrete,  though 
this  may  not  always  be  the  case.  The  grading  of  the  sand  should 
be  such  as  to  reach  maximum  density  when  combined  in  proper 
proportions  with  the  coarse  aggregate  to  be  used  in  the  concrete. 

Coarse  Aggregate. — This  may  consist  of  any  hard  mineral  sub- 
stance broken  to  proper  size — usually  broken  stone  or  gravel,  although 
sometimes  broken  slag,  cinders,  or  broken  brick  is  used. 

The  value  of  stone  as  an  aggregate  depends  upon  much  the  same 
qualities  as  are  needed  for  building  stone.  For  high-class  concrete 
work,  it  is  important  that  the  stone  should  possess  strength,  and 
absorb  but  little  water.  Stones  breaking  to  cubical  shapes  give 
better  results  than  those  of  shaly  or  slaty  character,  while  rounded 
pieces  pack  closer  and  show  less  voids  than  those  with  sharp  corners. 

Trap  and  granite  are  usually  the  best  of  concrete  materials. 
When  the  concrete  is  to  be  subjected  to  abrasive  wear,  trap  is  a 
superior  material.  For  resistance  to  direct  compression,  good  granite 

110 


AGGREGATES  FOR  CONCRETE  111 

is  to  be  preferred.  Limestones  and  sandstones  vary  greatly  in  their 
values  as  concrete  materials,  hard  limestones  and  some  of  the  more 
compact  sandstones  being  desirable  materials,  while  the  softer  vari- 
eties are  not  generally  suitable  for  first-class  concrete  work.  Gravel, 
when  of  flint  or  other  hard  material,  may  make  excellent  concrete. 

Sizes  for  Broken  Stone. — The  sizes  to  which  concrete  stone  should 
be  broken  depends  upon  the  use  to  which  the  concrete  is  to  be  put. 
In  heavy  walls  or  massive  work,  the  upper  limit  of  size  may  be  2  or 
3  inches  in  diameter.  It  is  desirable  to  have  the  stones  as  large 
as  can  be  easily  incorporated  into  the  mixture.  In  reinforced  work, 
where  the  concrete  must  pass  between'  and  under  the  reinforcing 
rods^  it  may  not  be  feasible  to  use  stone  of  more  than  1  inch  diameter. 

In  stone  or  gravel  for  coarse  aggregate,  as  in  sand  for  mortar, 
the  grading  of  sizes  should  be  such  as  to  give  maximum  density. 
For  a  given  stone,  the  strongest  concrete  will  ordinarily  be  made 
by  that  arrangement  of  sizes  which  requires  the  least  mortar  to 
completely  fill  the  voids  in  the  stone,  as  a  surplus  of  mortar  beyond 
that  required  for  completely  filling  the  voids  is  an  element  of  weak- 
ness in  the  concrete,  as  well  as  a  waste  of  the  more  expensive  materials. 
Stone  as  ordinarily  used  in  concrete  contains  all  sizes,  from  the 
largest  allowed  to  the  size  of  the  largest  sand.  All  material  retained 
on  a  J-  or  f-inch  screen  is  commonly  regarded  as  coarse  aggregate, 
and  stone  is  used  as  it  comes  from  the  crusher  with  all  the  sizes 
included,  only  the  chips  being  screened  out. 

Gravel  containing  sand  is  sometimes  used  without  screening  by 
mixing  with  cement.  This  is  not  desirable  practice,  as  the  sand  is 
seldom  in  proper  quantity  or  uniformly  distributed  through  the 
gravel,  it  should  be  screened  out  and  proportioned  properly  to  the 
cement  and  gravel. 

In  concrete  work  it  is  usually  necessary  to  use  the  materials 
available  in  the  locality  of  the  work,  but  where  important  work  is 
to  be  done,  careful  attention  should  be  given  to  the  character  of 
these  materials  and  of  the  concrete  made  from  them.  The  design 
of  concrete  structures  should  be  based  upon  full  information  concern- 
ing the  properties  of  the  concrete  to  be  used,  and  this  is  largely  a 
question  of  aggregates.  Poor  concrete  work  has  much  more  fre- 
quently resulted  from  the  use  of  poor  aggregates  than  from  the  use 
of  inferior  cement. 

In  many  cases  it  may  be  feasible  and  desirable  to  use  materials 
of  low  grade  in  concrete  work.  Cinder  concrete  is  preferred  for  some 
uses  on  account  of  its  lightness,  although  it  is  low  in  strength.  Local 
materials  may  be  of  poor  quality,  but  usable  by  taking  proper  pre- 


112  PLAIN  CONCRETE 

cautions  and  designing  the  work  in  accordance  with  the  character 
of  the  concrete.  Failures  have  sometimes  resulted  from  the  use 
of  low-grade  materials  without  investigation  of  their  qualities. 
Many  users  of  concrete  have  failed  to  recognize  the  importance  of 
the  quality  of  the  aggregates  and  seem  to  have  regarded  any  stone 
broken  to  proper  size  as  good  enough  for  concrete. 

72.  Tests  for  Coarse  Aggregates. — There  are  at  present  no 
standard  methods  of  making  tests  for  concrete  aggregates,  or  stand- 
ard specifications  for  such  materials.  The  methods  usually 
employed  in  testing  sand  have  been  discussed  in  Art.  7.  A  com- 
mittee of  the  American  Society  for  Testing  Materials  is  making  a 
study  of  concrete  aggregates  and  of  the  methods  of  testing  them, 
and  it  is  hoped  that  this  may  result  in  a  standard  practice  in  making 
such  tests,  and  in  throwing  light  upon  methods  of  proportioning 
and  forming  the  concrete. 

Mechanical  Analysis.  —  To  determine  the  relative  quantities  of 
various  sizes  of  stone  in  aggregate,  it  is  common  to  make  a  mechan- 
ical analysis  of  the  material.  This  consists  in  separating  the  various 
sizes  by  screening,  and  recording  the  amount  retained  upon  each 
screen.  The  following  has  been  adopted  by  the  American  Society 
for  Testing  Materials,  upon  recommendation  of  its  Committee  on 
Road  Materials,  as  a  standard  method  for  making  a  mechanical 
analysis  of  broken  stone  or  broken  slag,  except  for  aggregates  used  in 
cement  concrete: 

The  method  shall  consist  of  (1)  drying  at  not  over  110°  C.  (230°  F.)  to  a  con- 
stant weight  a  sample  weighing  in  pounds  six  times  the  diameter  in  inches  of 
the  largest  holes  required;  (2)  passing  the  sample  through  such  of  the  following 
size  screens  having  circular  openings  as  are  required  or  called  for  by  the  specifi- 
cations, screens  to  be  used  in  the  order  named:  8.89  cm.  (3£  in.),  7.62  cm.  (3  in.), 
6.35  cm.  (2J  in.),  5.08  cm.  (2  in.),  3.81  cm.  (H  in.),  3.18  cm.  (1£  in.),  2.54  cm. 
(1  in.),  1.90  cm.  (f  in.),  1.27  cm.  (£  in.),  and  0.64  cm.  (\  in.);  (3)  determining 
the  percentage  by  weight  retained  by  each  screen;  and  (4)  recording  the  mechan- 
ical analysis  in  the  following  manner: 


Passing  0 . 64  cm.  ( J  in.)  screen 

Passing  1.27  cm.  (£  in.)  screen  and  retained  on  a  0.64  cm.  (\  in.) 

screen 

Passing  1.90  cm.  (f  in.)  screen  and  retained  on  a  1.27  cm.  (^  in.) 

screen 

Passing  2.54  cm.  (1  in.)  screen  and  retained  on  a  1.90  cm.  (f  in.) 

screen.. 


100.00 


AGGREGATES  FOR  CONCRETE  113 

For  materials  in  which  sand  is  combined  with  the  broken  stone 
or  broken  slag,  the  same  method  is  employed  together  with  the 
fine  sieves  used  for  sand  (see  Art.  7)  and  the  results  are  recorded 
in  the  same  manner,  beginning  with  the  200-mesh  sieve. 

Apparent  Specific  Gravity. — The  weight  of  a  given  volume  of  the 
solid  material  of  which  the  aggregate  is  composed  is  often  of  impor- 
tance in  the  determination  of  voids,  or  in  proportioning  concrete, 
a  result  obtained  by  determining  the  apparent  specific  gravity.  The 
term  apparent  specific  gravity  as  here  used  refers  to  the  material 
as  it  exists,  and  includes  the  voids  in  the  block  of  material  tested; 
it  may  be  somewhat  less  than  the  true  specific  gravity.  For  this 
purpose,  the  water  to  which  it  is  referred  need  not  be  distilled,  and 
determinations  at  ordinary  air  temperatures  are  sufficiently  accurate. 

The  following  method  of  determining  apparent  specific  gravity 
of  coarse  aggregates  has  been  adopted  as  standard  by  the  American 
Society  for  Testing  Materials. 

The  apparent  specific  gravity  shall  be  determined  in  the  follow- 
ing manner: 

1.  The  sample,  weighing  1000  g.  and  composed  of  pieces  approximately 
cubical  or  spherical  in  shape  and  retained  on  a  screen  having  1.27  cm.  (£  in.) 
circular  openings,  shall  be  dried  to  constant  weight  at  a  temperature  between 
100  and  110°  C.  (212  and  230°  F.),  cooled,  and  weighed  to  the  nearest  0.5  g. 
Record  this  weight  as  weight  A.     In  the  case  of  homogeneous  material,  the 
smallest  particles  in  the  sample  may  be  retained  on  a  screen  having  1|  in.  cir- 
cular openings. 

2.  Immerse  the  sample  in  water  for  twenty-four  hours,  surface-dry  individual 
pieces  with  the  aid  of  a  towel  or  blotting  paper,  and  weigh.      Record  this  weight 
as  weight  B. 

3.  Place  the  sample  in  a  wire  basket  of  approximately  |  in.  mesh,  and  about 
12.7  cm.  (5  in.)  square  and  10.3  cm.  (4  in.)  deep,  suspend  in  water  1  from  center 
of  scale  pan,  and  weigh.   Record  the  difference  between  this  weight  and  the  weight 
of  the  empty  basket  suspended  in  water  as  weight  C.     (Weight  of  saturated 
sample  immersed  in  water.) 

4.  The  apparent  specific  gravity  shall  be  calculated  by  dividing  the  weight 
of  the  dry  sample  (A)  by  the  difference  between  the  weights  of  the  saturated 
sample  in  air  (B)  and  in  water  (C),  as  follows: 


Apparent  Specific  Gravity  = 


B-C 


5.  Attention  is  called  to  the  distinction  between  apparent  specific  gravity 
and  true  specific  gravity.  Apparent  specific  gravity  includes  the  voids  in  the 
specimen  and  is  therefore  always  less  than  or  equal  to,  but  never  greater  than 
the  true  specific  gravity  of  the  material. 

i  The  basket  may  be  conveniently  suspended  by  means  of  a  fine  wire  hung  from  a  hook 
shaped  in  the  form  of  a  question  mark  with  the  top  end  resting  on  the  center  of  the  scale  pan. 


114 


PLAIN  CONCRETE 


The  specific  gravities  and  weights  per  cubic  foot  of  materials 
commonly  used  for  aggregates  are  approximately  as  follows: 


Specific  Gravity. 

Weight  per  Cubic 
Foot. 

Gravel 

2  65 

165 

Trap  .  . 

2.85-3.00 

178-187 

Granite        

2.65-2  80 

165-175 

Limestone 

2  50-2  75 

155-170 

Compact  sandstone 

2  45-2  70 

153-168 

Porous  sandstone  

2  .  10-2  .  40 

130-150 

Cinders               ....           ....           .    . 

1.40-1  60 

90-100 

Determination  of  Voids. — The  voids  in  coarse  material,  such  as 
gravel  or  broken  stone  not  containing  sand  or  other  fine  material, 
may  be  obtained  by  filling  a  measure  of  known  volume  with  the 
material,  and  pouring  in  water  until  the  measure  is  full. 

The  volume  of  water 

Then,  the  percentage  of  voids  =  —  —  X 100. 

The  total  volume 

When  the  specific  gravity  of  the  material  is  known,  the  voids 
may  be  obtained  by  weighing  a  measured  volume  of  the  broken 
stone,  subtracting  this  weight  from  the  weight  of  an  equal  volume 
of  the  solid  material,  and  dividing  by  the  solid  weight. 

If  the  aggregate  contains  fine  material,  the  methods  used  for 
sand  as  given  in  Art.  7  must  be  used. 

It  is  evident  that  the  percentage  of  voids  in  a  mass  of  broken 
material  is  not  a  fixed  quantity,  but  varies  with  the  arrangement 
of  the  pieces.  If  the  material  were  composed  of  equal  cubes,  it 
would  be  possible  to  place  them  side  by  side  so  as  to  leave  no  voids 
which  could  be  filled  by  smaller  material.  Poured  loosely  into  a 
measure,  such  cubes  would  probably  show  at  least  45  per  cent  of 
voids,  which  would  be  somewhat  modified  by  shaking  down  and 
compacting  the  mass. 

When  the  aggregate  contains  small  pieces  which  may  lie  in  the 
voids  of  the  larger  ones,  the  tendency  to  variation  in  results  according 
to  arrangement  is  greatly  reduced,  but  the  method  of  filling  the 
measure,  and  amount  of  shaking  that  is  given,  will  somewhat  affect 
the  results.  Commonly,  the  material  is  shoveled  into  the  measure 
and  lightly  shaken  to  get  what  may  be  a  fair  estimate  of  the  voids 
in  the  material  as  it  is  to  be  used. 

When  fine  material  is  introduced  into  a  coarse  aggregate  to  fill 
the  voids,  particles  of  the  fine  material  get  between  the  larger  pieces 


AGGREGATES  FOR  CONCRETE  115 

and  hold  them  apart  so  that  the  voids  to  be  filled  in  the  larger  material 
are  increased,  and  cannot  be  completely  filled.  This  is  shown  by 
the  fact  that  the  volume  of  the  mixture  is  greater  than  that  of  the 
coarse  aggregate  even  though  the  volume  of  fine  aggregate  used  is 
much  less  than  the  volume  of  voids  in  the  larger  material. 

Selection  of  Aggregates. — The  Joint  Committee  of  the  Engineer- 
ing Societies  on  Concrete  and  Reinforced  Concrete  makes  the  follow- 
ing recommendations  concerning  the  selection  of  aggregates  in  its 
1917  report. 

AGGREGATES 

Extreme  care  should  be  used  in  selecting  the  aggregates  for  mortar  and  con- 
crete, and  careful  tests  made  of  the  materials  for  the  purpose  of  determining 
the  quality  and  grading  necessary  to  secure  maximum  density  or  a  minimum 
percentage  of  voids.  Bank  gravel  should  be  separated  by  screening  into  fine 
and  coarse  aggregates  and  then  used  in  the  proportions  to  be  determined  by 
density  tests. 

(a)  Fine  aggregate  should  consist  of  sand,  or  the  screenings  of  gravel  or  crushed 
stone,  graded  from  fine  to  coarse,  and  passing  when  dry  a  screen  having  J  in. 
diameter  holes;  it  preferably  should  be  of  siliceous  material,  and  not  more  than 
30  per  cent  by  weight,  should  pass  a  sieve  having  50  meshes  per  1m ear  inch;  it 
should  be  clean,  and  free  from  soft  particles,  lumps  of  clay,  vegetable  loam,  or 
other  organic  matter. 

Fine  aggregate  should  always  be  tested  for  strength.  It  should  be  of  such 
quality  that  mortar  composed  of  1  part  Portland  cement  and  3  parts  fine  aggre- 
gate by  weight  when  made  into  briquettes,  prisms  or  cylinders  will  show  a  tensile 
or  compressive  strength,  at  an  age  of  not  less  than  seven  days,  at  least  equal  to 
the  strength  of  1 : 3  mortar  of  the  same  consistency  made  with  the  same  cement 
and  standard  Ottawa  sand.  If  the  aggregate  be  of  poorer  quality,  the  propor- 
tion of  cement  should  be  increased  to  secure  the  desired  strength.  If  the  strength 
developed  by  the  aggregate  in  the  1  :  3  mortar  is  less  than  70  per  cent  of  the 
strength  of  the  Ottawa  sand  mortar,  the  material  should  be  rejected.  In  testing 
aggregates  care  should  be  exercised  to  avoid  the  removal  of  any  coaling  on  the 
grains  which  may  affect  the  strength;  bank  sands  should  not  be  dried  before 
being  made  into  mortar,  but  should  contain  natural  moisture.  The  percentage 
of  moisture  may  be  determined  upon  a  separate  sample  for  correcting  weight. 
From  10  to  40  per  cent  may  be  required  in  mixing  bank  or  artificial  sands  than 
for  standard  Ottawa  sand^to  produce  the  same  consistency. 

Coarse  aggregate  should  consist  of  gravel  or  crushed  stone  which  is  retained 
on  a  screen  having  |  in.  diameter  holes,  and  should  be  graded  from  the  smallest 
to  the  largest  particles;  it  should  be  clean,  hard,  durable,  and  free  from  all  dele- 
terious matter.  Aggregates  containing  dust  and  soft,  flat,  or  elongated  particles 
should  be  excluded.  The  Committee  does  not  feel  waranted  in  recommending 
the  use  of  blast-furnace  slag  as  an  aggregate,  in  the  absence  of  adequate  data 
as  to  its  value,  especially  in  reinforced  concrete  construction.  No  satisfactory 
specifications  or  methods  of  inspection  have  been  developed  that  will  control  its 
uniformity  and  ensure  the  durability  of  the  concrete  in  which  it  is  used. 

The  aggregate  must  be  small  enough  to  produce  with  the  mortar  a  homo- 


116  PLAIN  CONCRETE 

geneous  concrete  of  sluggish  consistency  which  will  readily  pass  between  and 
easily  surround  the  reinforcement  and  fill  all  parts  of  the  forms.  The  maximum 
size  of  particles  is  variously  determined  for  different  types  of  construction  from 
that  which  will  pass  a  £-in.  ring  to  that  which  will  pass  a  1^-in.  ring. 

For  concrete  in  large  masses  the  size  of  the  coarse  aggregate  may  be  increased, 
as  a  larger  aggregate  produces  a  stronger  concrete  than  a  fine  one;  however, 
it  should  be  noted  that  the  danger  of  separation  from  the  mortar  becomes  greater 
as  the  size  of  the  coarse  aggregate  increases. 

Cinder  concrete  should  not  be  used  for  reinforced  concrete  structures  except 
in  floor  slabs  not  exceeding  8-foot  span.  It  also  may  be  used  for  fire  protection 
purposes  when  not  required  to  carry  loads.  The  cinders  should  be  composed 
of  hard,  clean,  vitreous  clinker,  free  from  sulphides,  unburned  coal  or  ashes. 


ART.  20.     PROPORTIONING   CONCRETE 

73.  Arbitrary  Proportions. — The  common  method  of  propor- 
tioning concrete  is  by  assuming  ratios  between  the  volumes  of  cement, 
sand,  and  coarse  aggregate.  These  proportions  are  varied  accord- 
ing to  the  character  of  the  work,  and  sometimes  are  adjusted  to  the 
qualities  of  the  materials.  A  formula  of  definite  proportions  does 
not  always  lead  to  the  same  result  unless  the  method  of  measuring 
the  materials  is  the  same,  as  cement  measured  loose  may  vary  con- 
siderably in  weight  for  the  same  volume.  A  barrel  of  cement  may 
measure  from  3.5  to  5  feet,  according  to  its  degree  of  compactness. 
It  is  desirable  to  follow  the  recommendation  of  the  Joint  Committee 
on  Concrete  and  take  one  sack  (94  pounds)  of  cement  as  a  cubic 
foot,  or  a  barrel  as  4  cubic  feet  in  measuring  the  materials. 

Specific  fixed  proportions  have  to  a  certain  extent  become  stand- 
ard in  ordinary  practice  for  various  kinds  of  work.  For  reinforced 
concrete  in  building  construction  and  where  it  is  necessary  to  develop 
considerable  strength,  the  porportions  of  1  part  cement,  2  parts 
sand,  ancl  4  parts  broken  stone  are  commonly  employed.  For 
positions  where  strength  is  of  special  importance,  as  in  column  con- 
struction, or  work  in  light  superstructures  of  buildings,  the  propor- 
tions 1  :  1J  :  3,  or  sometimes  1:1:2,  are  used.  In  more  massive 
work  and  where  only  compressions  are  to  be  carried  with  ample 
sections,  the  proportions  1:3:6  and  sometimes  1  :  2J  :  5  are 
employed. 

The  common  proportions  are  based  upon  the  requirement  that 
the  volume  of  fine  aggregates  shall  be  one-half  that  of  the  coarse 
aggregate.  For  materials  commonly  used,  this  gives  a  quantity 
of  mortar  sufficient  to  fill  compactly  the  interstices  in  the  coarse 
aggregate.  The  quality  of  the  mortar  is  varied  by  changing  the 
ratio  of  cement  to  fine  aggregate,  and  the  strength  of  the  concrete 


PROPORTIONING  CONCRETE  117 

varies  accordingly.  The  ratios  between  fine  and  coarse  aggregates 
are  often  varied  when  the  coarse  aggregates  contain  more  or  less 
voids  than  is  usual,  and  1:2:3,  1:3:5,  1:2:5  or  1:3:7  con- 
crete is  frequently  used. 

Good  results  have  been  obtained  in  practice  by  this  method  of 
proportioning,  when  proper  attention  has  been  given  to  the  quality 
of  the  aggregates.  More  careful  methods  of  adjusting  proportions 
would  often  be  more  economical,  and  equally  good  results  might 
sometimes  be  obtained  with  less  cost  for  materials.  Many  users 
of  concrete  employ  ordinary  proportions  for  all  concrete  irrespective 
of  the  character  of  the  materials,  and  a  wide  variation  in  the  quality 
of  the  concrete  is  frequently  the  result. 

74.  Proportioning  by  Voids. — A  method  of  proportioning  some- 
times followed  is  to  determine  the  voids  in  the  aggregates,  and  use 
enough  cement  to  fill  the  voids  in  the  fine  aggregate  and  enough 
mortar  to  fill  the  voids  in  the  coarse  aggregate.  A  small  excess  of 
fine  materials  is  used  in  each  case  on  account  of  inequalities  of  mix- 
ing. If  the  fine  materials  would  all  lie  in  the  voids  of  the  larger 
materials,  this  method  would  always  give  the  desired  result,  and 
produce  the  concrete  of  maximum  density  and  greatest  strength. 
In  practice,  however,  the  voids  cannot  be  completely  filled,  the 
volumes  of  the  larger  materials  are  increased  by  the  smaller  par- 
ticles lying  between  them,  and  the  distribution  of  fine  material 
through  the  mass  is  not  uniform. 

Usually  a  volume  of  mortar  5  to  10  per  cent  in  excess  of  the  voids 
most  nearly  fills  the  voids  without  leaving  appreciable  excess  of 
mortar.  More  mortar  than  this  swells  the  volume  of  the  concrete 
without  increasing  density,  and  has  the  effect  of  weakening  the  con- 
crete. If,  for  instance,  sand  containing  50  per  cent  voids  is  used 
with  stone  containing  40  per  cent  voids,  and  just  fills  the  voids  in 
the  stone  without  increasing  the  volume,  the  resulting  mixture  will 
have  20  per  cent  voids.  If  an  excess  of  sand  be  used,  this  excess 
will  give  an  increase  in  volume  having  50  per  cent  voids. 

This  method  of  proportioning  is  an  improvement  over  that  of 
arbitrary  selection  of  ratios,  and  usually  gives  approximately  the 
most  desirable  proportions.  Variations  in  the  relative  sizes  of  the 
materials,  however,  may  change  considerably  the  proportions  neces- 
sary to  give  the  most  dense  concrete.  A  certain  sand  may  easily 
work  into  the  voids  of  a  given  broken  stone  without  materially 
increasing  its  volume,  while  with  another  stone  containing  the  same 
percentage  of  voids  but  of  different  sizes,  the  same  sand  may  produce 
quite  different  results,  and  to  secure  greatest  density  would  need 


118 


PLAIN  CONCRETE 


to  be  differently  proportioned.  The  object  should  be  to  get  the 
greatest  density  in  the  final  mixture  of  fine  and  coarse  aggregates. 

The  inaccuracies  involved  in  proportioning  cement  to  sand  by 
determining  the  voids  in  the  sand  is  explained  in  Art.  7.  When 
determining  the  ratio  of  fine  to  coarse  aggregates  by  the  method 
of  voids,  it  is  usual  to  proportion  cement  to  sand  by  adopting  an 
arbitrary  ratio  between  the  two,  although  some  users  of  concrete 
have  used  the  void  method  for  this  purpose  also. 

75.  Proportioning  by  Mechanical  Analysis  Curves. — Mr.  William 
B.  Fuller  l  has  devised  a  method  of  proportioning  concrete  by  plot- 
ting the  curves  of  mechanical  analysis  of  the  aggregates  to  be  used, 
then  combining  them  in  such  proportions  as  to  give  a  curve  which 
corresponds  as  nearly  as  possible  with  a  certain  ideal  curve.  This 
ideal  curve  is  supposed  to  represent  the  combination  of  sizes  which 
will  give  maximum  density  for  the  given  materials. 

Mechanical  Analysis  Curve. — The  method  of  plotting  the  curves 
of  mechanical  analysis  is  shown  in  Fig.  44.  The  analyses  are  made 


100 


.50  .75  LOO  |.£5 

DIAMETER  OF  PARTICLES  IN  INCHES 

FIG.  44. — Curves  of  Mechanical  Analyses. 


1.5 


by  the  method  outlined  in  Section  72.     In  the  curves,  the  ordinates 
represent  percentages  of  the  samples  (by  weight)  which  pass  through 

1  An  explanation  of  this  method  of  proportioning  is  given  by  Mr.  Fuller  in 
Taylor  and  Thompson's  "Concrete,  Plain  and  Reinforced,"  Third  edition, 
Chapter  X. 


PROPORTIONING  CONCRETE 


119 


openings  whose  sizes  are  shown  by  their  distances  from  the  origin. 
Fig.  44  shows  a  sample  of  stone  and  one  of  sand  which  are  to  be  used 
in  forming  concrete. 

'From  these  curves,  others  may  be  drawn  showing  the  grading 
of  sizes  in  various  combinations  of  cement,  sand,  and  stone.  Thus 
for  the  1:3:6  concrete,  we  will  have  percentages  passing  openings 
as  follows: 


Sizes  of  Openings, 
inches. 

PERCENTAGES  PASSING. 

Cement. 

Sand. 

Stone. 

Total. 

1.50 

10 

+     30 

+     60 

=  100 

1.25 

10 

+     30 

+  .80X60 

=  88 

1.00 

10 

+     30 

+  .53X60 

=  71.8 

.75 

10 

+     30 

+  .37X60 

=  62.2 

.50 

10 

+     30 

+  .15X60 

=  49 

.25 

10 

+  .97X30 

+  .03X60 

=  41 

.10 

10 

+  .88X30 

+     00 

=  36.4 

.05 

10 

+  .70X30 

+     00 

=  31 

.02 

10 

+  .40X30 

+     00 

=  22 

This  curve,  corresponding  to  10  per  cent  cement,  30  per  cent  sand, 
and  60  per  cent  stone,  is  shown  on  the  diagram,  as  is  the  curve  for 
1  :  2J  :  6J  concrete. 

The  ideal  curve  is  found  by  sifting  the  stone  and  sand  into  a 
number  of  sizes,  and  then  recombining  these  sizes  in  varying  pro- 
portions and  comparing  the  results,  until  the  condition  of  maximum 
density  is  obtained.  In  an  extended  series  of  experiments,  Messrs. 
William  B.  Fuller  and  Sanford  E.  Thompson  l  found  that  the  curve 
of  most  desirable  grading  of  materials  was  a  smooth  curve,  consist- 
ing of  an  ellipse  at  the  fine  end  with  a  straight  line  tangent  to  the 
ellipse  and  passing  through  the  point  where  100  per  cent  is  reached. 
The  materials  tested  in  these  experiments  consisted  of  broken  stone, 
gravel,  and  sand  used  in  the  construction  of  the  Jerome  Park  Reser- 
voir, at  New  York.  The  equation  for  the  ellipse  as  determined 
from  these  experiments  is 


x  and  y  being  the  horizontal  and  vertical  coordinates  of  points  on 
the  ellipse  measured  from  the  origin  of  the  diagram. 


Transactions,  American  Society  of  Civil  Engineers,  Vol.  LIX,  p.  67. 


120  PLAIN  CONCRETE 

The  values  of  a  and  b  vary  for  the  different  materials  and  are 
as  follows: 


Materials. 

a 

b 

Jerome  Park  stone  and  screenings  

0.  035-0.  14D 

29  4-2  2D 

Cow  Bay  gravel  and  sand        

0.04  -0.16D 

26  4-1  3D 

Jerome  Park  stone  and  Cow  Bay  sand   .      .    . 

0  04  -0  16D 

28  5-1  3D 

D  in  the  above  formulas  is  the  maximum  diameter  of  the  coarse 
aggregate. 

To  use  this  method  of  proportioning  it  is  first  necessary  to 
determine  the  ideal  curve.  Sufficient  data  are  not  available  to 
indicate  whether  the  formulas  given  above  are  generally  represent- 
ative of  broken  stone  and  gravel  respectively.  To  determine  the 
curve  in  a  particular  case,  the  sand  and  stone  should  each  be  sifted 
into  about  three  sizes.  A  trial  curve  may  then  be  assumed  and 
the  materials  mixed  in  proportions  to  agree  with  the  curve  and  the 
density  of  the  mixture  tested.  Curves  above  and  below  the  first 
one  can  be  tried  until  an  approximate  density  is  located. 

76.  Proportioning  by  Trial. — The  simplest  and  usually  the  most 
accurate  way  of  determining  the  ratios  of  quantities  of  materials 
for  concrete  is  that  of  mixing  batches  in  different  proportions  and 
comparing  the  densities  of  the  resulting  concrete.  The  object 
should  be  to  secure  the  mixture  of  aggregates  which  will  give  the 
greatest  density  when  mixed  with  the  cement  and  water. 

For  making  these  tests,  it  is  convenient  to  use  a  cylindrical 
measure  8  or  10  inches  in  diameter  and  12  or  15  inches  high.  A 
batch  of  concrete  is  mixed  in  assumed  proportions  to  the  consistency 
to  be  used  in  the  work,  and  the  height  to  which  it  fills  the  cylindrical 
measure  is  noted.  Other  batches  are  then  prepared  with  the  same 
total  weight  of  materials,  but  differing  in  proportions  of  aggregates, 
and  measured  in  the  same  manner.  The  greatest  density  is  that 
which  occupies  the  least  volume  for  the  same  weight.  It  is  necessary 
to  use  a  uniform  method  of  filling  the  cylinders,  and  is  usually  desir- 
able to  compact  the  concrete  by  light  ramming  in  rather  thin  layers 
to  prevent  voids  being  left  where  the  concrete  is  in  contact  with  the 
surface  of  the  cylinder. 

Amount  of  Cement. — In  this  method  of  porportioning,  as  in  the 
preceding  methods,  the  object  is  to  determine  the  proper  propor- 
tions of  aggregates  to  give  the  most  dense  concrete.  In  each  case, 
the  amount  of  cement  to  be  used  is  assumed  as  a  definite  ratio  to 


PROPORTIONING  CONCRETE  121 

the  total  weight  of  aggregates.  This  ratio  depends  upon  the  char- 
acter of  the  work  and  the  need  for  strength  in  the  concrete,  and  is 
determined  as  mentioned  in  Section  82.  In  many  instances,  on 
important  work,  it  is  desirable  to  test  the  strength  of  the  concrete 
as  well  as  the  density  and  modify  the  proportion  of  cement  to  suit 
the  requirements.  With  different  aggregates  the  strength  may  be 
quite  different  when  the  same  proportion  of  cement  is  used,  and 
economy  in  the  use  of  cement  may  result  from  determination  of  the 
actual  strength  of  concrete  with  varying  proportions  of  cement  to 
aggregate.  (See  Section  102.) 

More  cement  is  usually  required  to  produce  the  same  strength 
when  the  sizes  of  the  coarse  aggregates  are  small  than  when  larger 
aggregates  are  used.  Stone  broken  to  pass  a  f-inch  screen  may 
require  20  to  25  per  cent  more  cement  for  the  same  strength  than 
the  same  stone  broken  to  pass  a  1.5-inch  screen. 

77.  Fineness  Modulus  and  Surface  Area. — Several  studies  of 
methods  of  proportioning  concrete  have  recently  been  made,  involving 
extensive  experimental  investigations  and  resulting  in  suggestions 
of  new  methods.  The  tests  of  Mr.  D.  A.  Abrams  in  the  Structural 
Materials  Laboratory  at  the  Lewis  Institute  at  Chicago  led  to  the 
conclusion  that,  for  a  given  ratio  of  cement  to  aggregate,  the  pro- 
portions requiring  the  least  water  to  produce  the  required  consistency 
would  give  the  greatest  strength.  This  would  depend  primarily 
upon  the  grading  of  the  aggregate  in  size,  and  Mr.  Abrams  evolved 
a  method  by  the  use  of  what  he  calls  the  "  fineness  modulus,"  based 
upon  the  mechanical  analysis  of  the  aggregate.  The  Tyler  series 
of  sieves  is  used,  Nos.  100,  48,  28,  14,  8,  4,  etc.,  each  of  which  has 
openings  twice  the  diameter  of  those  of  the  preceding  ones.  Mr. 
Abrams  method  is  given  in  Bulletin  No.  1  of  the  Structural  Materials 
Research  Laboratory. 

Mr.  L.  N.  Edwards  has  proposed  1  a  method  of  proportioning 
concrete  by  means  of  the  surface  areas  of  the  particles  of  aggregate. 
A  theoretical  study  of  this  method  of  proportioning  has  been  made 
by  Mr.  R.  B.  Young,2  in  which  he  claims  that  the  quantity  of  water 
necessary  to  bring  a  concrete  mixture  to  a  given  consistency  is  de- 
pendent upon  the  surface  area  of  the  aggregates. 

These  and  other  investigations  in  progress  are  throwing  much 
light  upon  the  subject  of  proportioning  concrete  and  upon  its  qualities. 
The  concrete  is  affected  by  a  number  of  elements,  ea^h  of  which 
must  be  considered  in  determining  the  best  proportions.  The  ratio 

1  Proceedings,  American  Society  for  Testing  Materials,  1918,  Part  II. 

2  Proceedings,  American  Society  for  Testing  Materials,  1919,  Part  II. 


122  PLAIN  CONCRETE 

of  cement  to  aggregate,  the  voids  in  the  aggregates,  the  surface 
areas  of  the  aggregates,  the  quantity  of  water  used  in  mixing  are 
all  important,  and  are  all  directly  concerned  with  the  grading  of 
sizes  of  aggregates.  Some  method  based  upon  mechanical  analysis 
may  finally  be  standardized  for  general  use,  when  the  relative  impor- 
tance of  the  various  factors  are  more  fully  understood.  Any  of  the 
methods  proposed  may  be  employed  as  a  guide  in  selecting  propor- 
tions, but  actual  trial  of  the  materials  in  concrete  is  necessary  to 
give  certainty  in  results. 

78.  Yield  of  Concrete. — The  quantities  of  materials  needed  for 
a  cubic  yard  of  concrete  vary  with  the  amount  of  voids  in  the  aggre- 
gates and  the  proportions  in  which  they  are  combined  The  sizes 
of  the  aggregates  and  the  quantity  of  water  used  in  mixing  also 
influence  the  yield  of  concrete. 

Concrete  is  made  up  of  a  mixture  of  cement,  fine  aggregate, 
and  coarse  aggregate,  or  it  is  a  mixture  of  cement  mortar  with  coarse 
aggregate.  The  volume  of  the  concrete  is  the  sum  of  the  volumes 
of  the  mortar,  the  solid  material  in  the  coarse  aggregate  and  the 
unfilled  voids  in  the  coarse  aggregate. 

Let  C  =  Volume  of  cement  in  cubic  feet  (bags  of  94  pounds  each) ; 

S  =  Volume  of  fine  aggregate  in  cubic  feet ; 

R  =  Volume  of  coarse  aggregate  in  cubic  feet ; 

F= Volume  of  voids  in  coarse  aggregate  in  cubic  feet; 
s= Ratio  of  sand  to  cement  =  S/C] 
r= Ratio  of  coarse  aggregate  to  cement  =  R/C; 
v  =  Ratio  of  voids  to  total  volume  of  coarse  aggregate,  V/R. 

The  quantities  of  ingredients  necessary  to  produce  given  volumes 
of  cement  mortars,  and  the  variations  for  different  materials,  are 
discussed  in  Section  34,  and  while  these  quantities  vary  considerably 
with  different  materials,  the  volume  of  mortar  produced  by  the 
mixture  of  different  proportions  of  cement  and  sand  is  fairly  well 
expressed  by  the  expression : 

Volume  of  mortar  =  aC+6$, 

in  which  a  and  b  are  coefficients  depending  upon  the  character  of 
the  sand.  The  volume  of  concrete  from  given  quantities  of  cement, 
sand  and  stone  may  then  be  expressed  by  the  formula : 

Q  =  aC+bS+c(R-V), 

in  which  c  is  a  coefficient  depending  upon  the  amount  of  unfilled 
voids  in  the  stone.  For  ordinary  fairly  coarse  sands  commonly 


PROPORTIONING  CONCRETE  123 

used  for  concrete,  a  may  be  taken  .67  and  b  .77.  For  well  compacted, 
plastic  concrete  of  ordinary  materials,  c  is  about  1.10.  With  these 
values  of  the  coefficients,  the  formula  becomes: 


or 

Q  =  C[.67+.77H-l.lr(l-t;)]. 

The  volume  of  cement  required  to  make  a  cubic  yard  of  concrete 
is: 


The  number  of  barrels  of  cement  =  C/4. 
Cubic  yards  of  sand  =  Cs/27, 
cubic  yard  of  stone  =  Cr/27. 

Table  VI  gives  approximate  quantities  of  materials  required  for 
1  cubic  yard  of  plastic  concrete,  using  stone  with  differing  percent- 
ages of  voids.  Average  crusher  run  stone,  with  chips  removed,  has 
about  40  to  45  per  cent  voids;  good  natural  gravel,  screened,  may 
have  35  to  40  per  cent  voids;  mixed  stone  and  gravel  often  runs 
from  30  to  35  per  cent  voids,  while  carefully  graded  materials  may 
have  voids  reduced  to  from  20  to  30  per  cent. 

Variations  in  the  characters  of  the  materials  used,  and  in  the 
methods  of  handling  and  placing  the  concrete  may  vary  considerably 
the  quantities  of  materials  required.  Dry  concrete,  if  thoroughly 
compacted  by  ramming,  is  more  dense  and  occupies  less  space  than 
plastic  or  wet  concrete,  but  as  ordinarily  placed  is  more  porous  and 
occupies  more  space.  Fine  sand  swells  more  when  mixed  with 
cement  and  water,  and  fills  more  space  in  plastic  concrete,  than 
coarse  sand.  Coarse  broken  stone  compacts  in  concrete  so  as  to 
leave  less  unfilled  voids  than  smaller  stone  with  the  same  per  cent 
of  voids.  Poor  work,  such  as  irregular  mixing  or  imperfect  com- 
pacting, results  in  more  porous  concrete  and  requires  less  materials. 

Tests  of  the  yield  of  concrete  may  easily  be  made  by  mixing  a 
batch  in  the  proportions  to  be  used  and  measuring  the  resulting 
concrete.  In  cases  where  accurate  estimates  of  quantities  are  impor- 
tant and  data  concerning  the  particular  materials  are  not  at  hand, 
such  tests  should  be  made. 


124 


PLAIN  CONCRETE 


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MIXING  CONCRETE  125 

ART.   21.     MIXING   CONCRETE 

79.  Preparation  of  Materials. — In  making  concrete,  the  materials 
should  be  properly  prepared  and  conveniently  placed  for  use,  as  the 
labor  cost  of  concrete  work  is  largely  a  matter  of  arrangements  for 
handling  materials.  The  work  should  be  systematized  so  that  it 
goes  forward  smoothly,  without  loss  of  time  in  any  of  its  parts. 

Broken  stone  can  usually  be  obtained  within  such  range  of  sizes 
as  may  be  desired.  In  preparing  crushed  stone,  the  crusher  is  set 
to  the  maximum  size  allowed,  and  the  product  varies  from  this  size 
to  dust.  This  product  is  then  passed  through  rotary  screens  inclined 
at  a  small  angle  to  the  horizontal,  which  are  made  in  sections  of 
different  sizes  of  openings,  and  admit  of  screening  the  stone  into 
several  sizes  at  one  operation.  When  considerable  quantities  of 
materials  are  being  used,  the  cost  of  handling  the  stone  may  not  be 
materially  increased  by  using  several  sizes  and  grading  the  aggregate. 
In  any  case  where  the  aggregates  available  are  badly  graded,  the 
advantage  to  be  gained  by  grading  them  should  be  carefully  con- 
sidered. 

The  screened  stone  usually  drops  from  the  screens  into  bins, 
which  are  arranged  so  that  the  contents  may  be  drawn  off  through 
chutes  into  cars  or  wagons  for  transportation  to  the  work.  The 
sizes  and  arrangement  of  the  bins  depend  upon  the  need  for  storage 
and  the  kind  of  transportation.  It  is  usually  desirable  that  the  bins 
be  of  sufficient  size  to  equalize  variations  in  the  rate  of  use,  or  short 
delays  in  the  crushing  plant,  so  that  work  may  proceed  continuously. 

Gravel  and  sand  nearly  always  need  to  be  screened.  When  con- 
siderable quantities  are  to  be  handled,  and  power  for  operating  the 
screen  is  available,  rotary  screens  are  desirable,  giving  the  most 
economical  handling  of  the  material,  and  admitting  of  division  into 
required  sizes. 

In  small  work  it  is  usual  to  employ  hand  screens,  which  are  set 
up  in  an  inclined  position,  and  the  material  thrown  against  them 
with  a  shovel,  the  finer  material  passing  through  and  the  coarser 
sliding  down  to  the  foot  of  the  screens.  Sometimes  two  or  more 
inclined  screens  are  placed  so  that  the  material  which  passes  one 
falls  upon  the  one  below,  each  being  hinged  so  that  its  inclination 
to  the  horizontal  may  be  adjusted. 

Sand  and  gravel  frequently  require  washing  to  remove  dirt  and 
fine  material,  which  is  often  accomplished  by  supplying  water  in 
the  chutes  leading  to  the  screens,  the  dirt  being  washed  through  a 
fine  screen  which  retains  the  aggregate.  Sometimes  the  material 


126  PLAIN  CONCRETE 

is  washed  down  a  sloping  trough,  with  a  fine  screen  set  in  its  bottom 
to  permit  the  dirt  to  pass  through.  Portable  plants  for  screening 
and  washing  are  available  hi  a  number  of  forms,  and  often  provide 
the  most  economical  means  of  handling  work  of  this  kind.  Wetting 
the  material  while  in  a  pile,  for  the  purpose  of  cleaning  it,  is  useless. 

Some  storage  of  materials  where  the  work  is  to  be  done  is  usually 
necessary,  in  order  to  have  a  supply  which  permits  work  to  proceed 
continuously.  The  location  of  the  materials  with  reference  to  the 
mixer,  or  mixing  platform,  should  be  carefully  considered,  as  their 
convenience  to  the  work  affects  the  cost  of  mixing  the  concrete. 
The  amount  of  storage  should  be  as  small  as  is  consistent  with  assur- 
ing a  continuous  supply  to  the  mixers. 

80.  Hand  Mixing. — Concrete  may  be  mixed  by  any  method 
which  will  produce  a  homogeneous  mass  of  uniform  consistency. 
The  arrangement  of  the  work  and  methods  of  manipulating  the 
materials  in  hand  mixing  vary  greatly  with  the  character  of  the  con- 
struction and  the  ideas  of  the  men  in  charge.  The  costs  vary  as 
widely  as  the  methods. 

Measuring  the  Materials. — Bottomless  boxes  are  sometimes  used 
for  measuring  the  aggregates,  the  box  being  placed  on  the  mixing 
platform,  filled,  and  then  removed,  leaving  the  material  on  the  plat- 
form— an  accurate  means  of  measuring,  and  desirable  when  it  can 
be  employed  without  materially  increasing  the  cost  of  handling  the 
aggregates. 

Measuring  in  wheelbarrows  is  commonly  employed,  and  fre- 
quently results  in  very  irregular  proportioning,  as  the  barrow  may 
not  always  be  equally  filled,  unless  special  attention  be  given  to  the 
loading.  When  this  method  is  employed,  it  is  desirable  to  have 
barrows  of  such  form  that  they  may  be  evenly  filled  to  level  surface. 
When  ordinary  barrows  are  used,  a  bottomless  box  may  be  placed 
in  the  barrow,  filled  and  removed,  before  starting  with  the  load. 
It  is  worth  while  to  use  a  method  that  will  give  accurate  measure- 
ment, even  at  a  small  extra  cost  for  labor. 

Cement  is  measured  by  counting  bags. 

The  mixing  of  concrete  by  hand  should  be  done  upon  a  water- 
tight platform.  The  cement  and  sand  should  first  be  mixed  dry, 
being  turned  by  shovels,  or  worked  by  hoes,  until  the  mixture  has 
uniform  color.  Water  may  then  be  added  and  the  mixture  worked 
into  a  rather  soft  mortar,  after  which  the  stone  is  wheeled  or  shoveled 
on  top  of  the  mortar  and  the  whole  turned  with  shovels  until 
thoroughly  mixed.  When  this  method  is  followed  the  stone  should 
be  wet,  to  prevent  taking  the  water  from  the  mortar. 


MIXING  CONCRETE  127 

After  mixing  the  sand  and  cement  dry,  the  stone  may  be  immedi- 
ately distributed  over  the  top  of  the  mixture,  water  added,  and  the 
whole  mixed  by  turning  with  shovels.  In  mixing  concrete  the  shovels 
must  be  turned  completely  over  and  the  contents  deposited  bottom 
side  up.  It  is  often  difficult  for  workmen  who  have  used  shovels  in 
other  work  to  get  the  knack  of  doing  this.  Until  they  do,  they 
accomplish  very  little. 

Water  should  be  poured  on  from  buckets  and  care  used  to  get 
only  the  quantity  needed  to  properly  mix  the  concrete.  The 
quantity  of  water  to  be  used  depends  upon  the  character  of  the  work 
and  manner  of  placing  the  concrete.  An  excess  of  water  beyond 
that  necessary  to  give  a  plastic  consistency  is  always  an  element  of 
weakness  in  the  concrete. 

Work  of  this  kind  always  requires  close  supervision  to  see  that 
all  of  the  operations  are  properly  performed  and  that  the  concrete 
produced  is  of  uniformly  good  quality.  Economy  in  hand  mixing 
depends  upon  the  work  being  so  organized  that  it  goes  smoothly 
in  all  its  parts,  every  man  having  his  regular  duties,  and  the  number 
of  men  at  each  kind  of  work  being  such  that  one  set  of  men  does  not 
have  to  stand  idle  waiting  for  others. 

81.  Machine  Mixing. — Machinery  is  now  used  for  mixing  in 
practically  all  large  concrete  construction,  and  it  is  rapidly  replacing 
hand  mixing  in  much  of  the  smaller  work.  Portable  plants,  which 
may  readily  be  moved  from  place  to  place,  are  making  this  economic- 
ally feasible.  There  are  a  large  number  of  mixers  on  the  market, 
differing  more  or  less  in  their  method  of  mixing  the  materials  or  in 
their  mechanical  appliances  for  handling  materials. 

Rotating  batch  mixers  are  either  cubical  boxes  mounted  to  rotate 
about  horizontal  axes  passing  through  two  opposite  corners,  or 
cylindrical  or  conical  drums  rotating  about  their  geometrical  axes. 
The  interior  of  the  mixer  is  usually  provided  with  blades,  causing 
the  materials  to  be  thrown  from  one  part  of  the  mixer  to  another 
by  the  rotation.  In  using  these  mixers,  the  materials  in  proper  pro- 
portions to  form  a  batch  of  concrete  are  put  into  the  hopper  of  the 
machine,  and  charged  into  the  mixer  at  one  time.  The  mixer  is  then 
run  for  a  sufficient  length  of  time  to  mix  the  ingredients,  thoroughly 
and  the  concrete  is  drawn  off  through  the  outlet.  The  amount 
of  water  required  should  be  determined,  and  measured  for  each 
batch.  Automatic  appliances  for  measuring  water  are  provided  on 
some  machines. 

The  proportions  of  materials  are  under  perfect  control  by  this 
method,  and  the  thoroughness  of  mixing  may  be  insured  by  regulat- 


128  PLAIN  CONCRETE 

ing  the  time  of  rotation  for  a  batch.  Examination  of  the  concrete  as 
it  comes  from  the  mixer  will  show  whether  it  is  thoroughly  mixed 
and  of  proper  consistency.  Some  operators  try  to  speed  the  work 
by  using  more  water  than  necessary  and  using  less  time  in  mixing. 
This  diminishes  the  strength  of  the  concrete  and  should  not  be 
allowed.  The  more  thoroughly  the  concrete  is  mixed,  the  less  the 
amount  of  water  required  to  produce  a  given  consistency,  and 
thoroughly  mixed  materials  flow  better  and  have  less  tendency  to 
separate  in  placing  than  those  made  soft  by  excess  of  water.  In 
most  cases  the  run  should  not  be  less  than  one  minute  properly  to 
mix  a  batch.  Some  machines  have  devices  for  automatic  control 
of  the  discharge  to  prevent  shortening  the  time  of  mix. 

Paddle  mixers,  consisting  of  a  series  of  paddles  mounted  on  a 
horizontal  shaft,  and  working  in  a  trough,  are  usually  employed  as 
continuous  mixers.  In  these,  the  materials  are  fed  in  at  one  end, 
forced  down  the  trough  by  the  paddles,  and  discharged  at  the  other 
end.  These  machines  have  not  usually  been  so  satisfactory  as  the 
batch  mixers,  on  account  of  the  lack  of  uniformity  in  supplying  the 
materials.  Some  automatic  feeding  appliances  have  been  found  to 
work  fairly  well,  and  when  the  supply  of  ingredients  can  be  evenly 
regulated  these  machines  may  do  good  work. 

Gravity  mixers  are  those  in  which  the  materials  are  mixed  by 
falling  through  a  vertical  or  inclined  chute,  and  striking  obstructions 
in  the  fall  which  throw  them  together.  This  mixer  requires  no 
power  for  operation,  but  the  materials  must  be  at  a  considerable 
elevation  to  provide  the  necessary  fall. 

The  cost  of  machine  mixing  depends  largely  upon  the  appliances 
used  in  conveying  the  materials  to  and  from  the  mixer  and  the  method 
of  feeding  the  mixer.  The  arrangement  of  a  mixing  plant  must 
depend  upon  the  character  and  amount  of  work  to  be  done  and  the 
topography  of  the  site.  When  the  work  is  large  arid  concentrated 
within  a  small  area,  a  plant  of  permanent  character  may  be  erected 
with  derricks  or  other  mechanical  appliances  for  handling  the  materi- 
als. Sometimes  a  plant  of  this  kind  is  made  semi-portable  by  erect- 
ing it  on  a  framework  resting  upon  wheels  or  rollers,  which  permit 
it  being  moved  as  the  work  progresses. 

It  is  very  common  to  have  the  mixer  set  so  that  it  may  discharge 
into  barrows  or  carts  on  the  ground,  the  materials  being  supplied 
by  wheelbarrows  from  piles  on  the  ground  near  the  mixer.  For 
this  purpose,  the  rotary  mixer,  with  movable  hopper  which  may  be 
let  down  to  the  ground  for  filling,  is  often  used,  portable  plants 
mounted  on  wheels  being  very  commonly  of  this  type.  Wheel- 


PLACING  CONCRETE  129 

barrows  with  the  wheel  under  the  body  of  the  barrow,  so  that  the 
barrow  may  be  easily  dumped  over  the  wheel,  are  convenient  for 
this  kind  of  work. 

In  building  construction,  the  mixer  is  commonly  at  the  surface 
of  the  ground  and  supplied  by  barrows,  the  concrete  being  delivered 
at  required  elevations  by  bucket  hoists. 

ART.   22.     PLACING   CONCRETE 

82.  Transporting  Concrete. — The  methods  of  handling  concrete 
from  the  mixer  to  its  final  location  vary  with  the  size  of  the  work 
and  the  consistency  of  the  concrete. 

For  small  work  and  short  distances,  wheelbarrows  are  commonly 
used.  Ordinary  contractors'  barrows  carry  from  about  1.8  to  2.0 
cubic  feet  at  a  load.  For  longer  hauls,  two-wheeled  barrows,  carry- 
ing about  6  cubic  feet,  are  more  economical.  On  large  work,  cars 
running  on  temporary  tracks  are  frequently  employed,  or  when  the 
work  is  within  a  short  radius,  derricks  may  be  used.  In  building 
operations  concrete  is  frequently  raised  by  a  bucket  hoist  to  the 
required  elevation  and  distributed  by  barrows  to  the  various  parts 
of  the  work. 

These  methods  of  handling,  in  which  a  small  bulk  of  the  concrete 
is  held  together  in  transportation  and  dumped  at  once  into  place, 
offer  little  opportunity  for  the  ingredients  of  the  concrete  to  separate. 
Well-mixed  concrete  of  any  proper  consistency  may  be  transported 
to  considerable  distances  without  being  injured.  Concrete  that 
is  so  dry  as  to  lack  cohesion,  or  concrete  that  is  so  wet  that  the  mor- 
tar is  soft  enough  to  run  away  from  the  stone,  shows  a  tendency  to 
separation  in  handling,  and  these  consistencies  should  not  be  used. 

Transportation  in  Chutes. — The  distribution  of  concrete  is  some- 
times effected  by  elevating  it  sufficiently  to  permit  it  to  flow  in  a 
trough  or  chute  to  its  destination,  and  by  arranging  a  system  of 
movable  chutes  it  is  often  possible  to  distribute  over  considerable 
area  from  a  single  hoisting  tower.  When  the  mixer  can  be  set  above 
the  work,  as  in  foundations  or  sometimes  in  dams  and  similar  struc- 
tures, the  concrete  may  be  transported  wholly  by  gravity. 

To  flow  in  chutes,  rather  soft,  mushy  concrete  is  necessary, 
unless  the  chutes  are  quite  steep.  When  the  slope  of  the  chute  is 
very  flat,  the  concrete  must  be  made  very  wet,  and  does  not  result 
in  first-class  work,  while  the  extra  water  necessary  to  make  the 
concrete  flow  on  a  flat  slope  causes  the  mortar  to  separate  from 
the  stone,  and  frequently  washes  portions  of  the  cement  from  the 


130  PLAIN  CONCRETE 

mortar.  The  practice  of  adding  water  in  the  chutes  to  assist  the 
flow  is  always  detrimental. 

Experience  indicates  that  concrete  may  be  made  to  flow  readily 
in  chutes  on  slopes  from  about  20°  to  35°  to  the  horizontal;  for 
any  slope  less  than  about  20°,  the  concrete  must  be  made  too  wet. 
The  mass  of  concrete  should  slide  along  the  chute  as  a  whole,  the 
stone  and  mortar  traveling  together  at  common  velocity.  For 
ordinary  mushy  concrete,  as  commonly  used  in  reinforced  work,  a 
slope  of  2  horizontal  to  1  vertical  is  found  most  efficient. 

Pneumatic  Transportation,  by  forcing  the  concrete  through  pipes 
by  compressed  air,  has  been  used  in  some  instances — a  method  avail- 
able on  congested  work,  where  space  is  lacking  for  other  means  of 
transport,  as  in  tunnel  and  subway  work.1 

83.  Depositing  Concrete. — When  concrete  is  mixed  dry  (the 
consistency  of  damp  earth)  and  placed  in  mass  construction,  it  is 
usually  placed  in  layers  about  6  inches  deep  and  each  layer  tamped 
until  the  mortar  flushes  to  the  surface.  Concrete  so  mixed  and  placed 
attains  greater  strength  than  if  mixed  with  more  water.  If  dry 
concrete  is  not  tamped  so  as  to  be  thoroughly  compacted,  it  is  more 
porous  and  has  less  strength  than  wet  concrete;  the  labor  required 
in  properly  placing  dry  concrete  is  considerable  and  the  work  strenu- 
ous, so  that  for  ordinary  uses  dry  concrete  is  not  commonly  employed. 
Poor  work  has  frequently  resulted  from  the  use  of  dry  concrete  not 
properly  compacted. 

In  ordinary  practice  concrete  is  mixed  either  to  a  rather  stiff 
plastic  condition  or  to  a  softer  mushy  consistency.  Plastic  con- 
crete, when  in  massive  work,  should  be  spread  in  layers  not  more 
than  10  or  12  inches  deep  and  lightly  rammed;  the  mortar  should 
readily  flush  to  the  surface  and  the  mass  quake  like  jelly  under  the 
ramming.  The  rammer  is  usually  a  flat  piece  of  iron  about  6  inches 
square,  with  a  vertical  handle,  and  weighing  15  to  20  pounds. 
Smaller  tapering  rammers  are  also  used  for  compacting  next  to  the 
forms. 

Mushy  concrete  may  be  deposited  in  somewhat  thicker  layers, 
being  lightly  tamped  or  worked  with  rammers  of  small  section, 
usually  about  2x3  inches,  for  the  purpose  of  eliminating  air  bubbles 
and  making  sure  that  there  are  no  open  spaces  unfilled  with  mortar. 
A  flat  spade  is  commonly  run  down  next  to  the  form  to  bring  the 
mortar  to  the  surface  and  prevent  voids  which  often  occur  where 
the  stones  of  the  concrete  are  in  contact  with  the  form. 

1  See  Engineering  and  Contracting,  March  17,  1915,  or  Engineering  News, 
March  16,  1916. 


PLACING  CONCRETE  131 

Laitance. — In  the  use  of  very  soft  concrete,  when  an  excess  of 
water  is  used,  there  is  a  tendency  for  certain  parts  of  the  cement 
to  be  taken  up  by  the  surplus  water  and  deposited  on  the  upper 
surface  of  the  concrete  as  a  sort  of  light-colored  slime,  which  is 
known  as  laitance.  Its  formation  involves  a  loss  of  cement  in  the 
concrete  and,  if  left  in  the  body  of  the  concrete,  it  forms  a  plane  of 
weakness  in  the  mass  of  concrete.  Laitance  is  often  found  to  an 
objectionable  extent  when  very  wet  concrete  is  chuted  to  place, 
and  deposited  in  masses  of  considerable  vertical  thickness.  A  column 
of  wet  concrete  poured  through  chutes  may  have  a  cap  of  laitance 
2  or  3  inches  thick  which  must  be  removed. 

.  Bonding  to  Old  Work. — Joints  must  frequently  be  made  with 
work  previously  placed.  In  massive  work,  subjected  only  to  com- 
pressive  stresses  normal  to  the  joints,  the  surface  of  the  old  concrete 
must  be  clean  and  should  be  wet  before  the  placing  of  the  new  con- 
crete. In  work  where  the  strength  of  the  bond  of  the  new  to  the  old 
work  is  of  special  importance,  the  old  work  should  be  cleaned,  all 
laitance  removed,  the  skin  on  smooth  surfaces  broken  by  scarifying, 
and  the  surface  thoroughly  wet.  A  coating  of  cement  paste  will 
then  aid  the  bond  with  the  new  work. 

Joints  between  different  days'  work  should  be  carefully  located 
where  they  will  be  least  injurious  to  the  strength  of  the  structure. 
When  feasible  it  is  desirable  to  divide  a  structure  into  integral  parts, 
each  of  which  may  be  constructed  without  stopping  the  work. 

Depositing  under  Water. — Concrete  work  for  under-water  con- 
struction is  sometimes  done  by  passing  the  mixed  concrete  through 
the  water  to  the  desired  position.  It  is  common  to  use  a  tremie  for 
this  purpose.  This  consists  of  a  tube  or  closed  chute,  which  is  kept 
full  of  concrete  so  that  the  water  has  no  chance  to  wash  the  concrete 
as  it  passes  downward.  The  bottom  of  the  tremie  is  moved  about 
over  the  surface  upon  which  the  concrete  is  being  deposited,  so  that 
the  concrete  does  not  fall  through  the  water.  Concrete  for  this 
purpose  must  be  quite  wet,  in  order  to  flow  readily  to  place  without 
being  washed  by  the  water  through  which  it  is  passing. 

Buckets,  which  are  filled  with  concrete,  lowered  through  the 
water,  and  dumped  by  opening  the  bottom  when  in  contact  with 
the  surface  upon  which  the  concrete  is  to  be  placed,  are  also  some- 
times used  for  under-water  work.  The  method  of  enclosing  the 
concrete  in  bags  and  placing  these  in  contact  with  each  other  has 
also  been  used  for  this  purpose. 

84.  Placing  Concrete  in  Freezing  Weather. — The  setting  and 
hardening  of  concrete  are  greatly  retarded  at  low  temperatures;  in 


132  PLAIN  CONCRETE 

cold  weather  much  longer  time  is  needed  to  gain  strength,  and  forms 
must  be  left  longer  before  removal.  Accidents  have  sometimes 
occurred  to  concrete  structures  through  premature  removal  of  forms, 
on  account  of  failure  to  consider  the  influence  of  temperature  upon 
the  rate  of  hardening.  At  40°  F.,  the  time  required  to  gain  a  given 
strength  is  two  or  three  times  as  long  as  at  70°  F.;  below  40°  F.. 
the  required  time  rapidly  increases  as  the  temperature  is  lowered. 

Cement  mortar  or  concrete  made  and  frozen  before  it  has  time  to 
set  is  uninjured  by  freezing  and  sets  and  hardens  properly  after  it 
thaws  out.  If  the  mortar  is  frozen  when  partially  set  or  soon  after 
it  has  set  and  before  any  considerable  strength  has  been  gained,  the 
expansion  caused  by  freezing  breaks  the  bond  and  destroys  the 
cohesion  of  the  mass,  causing  it  to  crumble  upon  thawing  out. 

The  use  of  concrete  in  freezing  weather,  except  in  large  masses, 
should  be  avoided  in  so  far  as  possible.  When  it  is  necessary  to 
place  concrete  at  freezing  temperature,  or  when  it  is  likely  to  be 
frozen  soon  after  placing,  extreme  care  should  be  taken  to  minimize 
the  probable  effect  of  freezing  upon  the  concrete.  The  methods 
employed  may  be  intended  to  hasten  the  setting  and  hardening  of 
the  cement,  to  prevent  the  concrete  from  freezing  soon  after  placing, 
or  both,  and  for  this  purpose,  materials  may  be  selected  that  will 
act  quickly  when  made  into  mortar.  Quick-setting  cements,  how- 
ever, are  sometimes  more  retarded  by  low  temperatures  than  others 
setting  more  slowly  at  normal  temperatures.  In  selecting  materials, 
it  is  more  important  to  get  those  acquiring  strength  quickly  than 
those  setting  quickly. 

Heating  the  Materials,  and  mixing  and  placing  them  warm,  has 
the  effect  of  hastening  the  hardening  processes,  and  also  prevents 
immediate  freezing.  If  the  temperature  is  but  little  (3°  or  4°)  below 
the  freezing-point,  heating  the  materials  and  placing  the  concrete 
warm  may  be  sufficient  to  prevent  injury  from  freezing.  Protec- 
tion should  also  be  given  the  concrete  to  delay  freezing  as  long  as 
possible.  The  materials  should  not  be  at  a  temperature  much  above 
100°  or  110°  F.  at  the  time  of  mixing.  The  use  of  hot  water  is 
injurious  to  the  cement,  and  may  defeat  the  object  of  heating  by 
preventing  the  cement  setting  properly. 

Having  placed  the  concrete  while  warm,  if  the  temperature  is 
likely  to  be  more  than  3°  or  4°  below  the  freezing-point,  it  is  neces- 
sary to  have  some  means  of  keeping  the  work  from  freezing  on  the 
surface,  which  may  sometimes  be  done  by  enclosing  the  work  in 
some  way  and  using  small  stoves,  or  steam  pipes  may  be  available 
for  heating  small  enclosed  spaces.  In  placing  work  in  large  masses, 


PLACING  CONCRETE  133 

the  heat  of  chemical  action  will  prevent  freezing  in  the  body  of  the 
work,  but  exposed  surfaces  must  be  protected. 

Use  of  Salt. — When  the  temperature  is  but  little  below  the  freez- 
ing-point, the  freezing  of  concrete  may  be  prevented  by  dissolving 
salt  in  the  water  used  for  mixing.  A  small  addition  of  salt  (3  to 
5  per  cent  of  the  weight  of  water)  lowers  the  freezing-point  of  the 
concrete,  and  prevents  injury  from  freezing  at  temperatures  perhaps 
5°  or  6°  below  freezing.  The  salt  also  has  the  effect  of  somewhat 
increasing  the  rapidity  of  hardening,  which  is  very  slow  at  such 
temperatures. 

Salt  is  sometimes  used  in  larger  proportion,  10  to  15  per  cent  of 
the  weight  of  water,  to  prevent  freezing  at  lower  temperatures. 
This  seems  to  retard  hardening,  and  is  considered  by  some  engineers 
to  be  harmful  to  the  concrete. 

85.  Contraction  Joints. — Cement  mortar  and  concrete  expand 
and  contract  with  changes  of  temperature  in  the  same  manner  as 
other  materials.  They  also  change  in  dimension  with  changes  in 
moisture,  expanding  when  wet  and  contracting  when  dry. 

Temperature  Changes. — The  coefficient  of  expansion  of  concrete 
has  been  found  by  various  investigators  to  vary  from  about  .0000050 
to  .0000065  per  degree  F.,  the  average  result  being  about  .0000055 
per  degree  F.,  or  .0000099  per  degree  C.  If  the  coefficient  of  elas- 
ticity of  the  concrete  is  2,000,000,  this  would  be  sufficient  to  produce 
a  unit  stress  in  the  concrete  of  440  lb./in.2,  for  a  change  of  temper- 
ature of  40°  F.  if  the  concrete  be  restrained  from  yielding. 

Concrete  in  large  masses  frequently  reaches  a  high  temperature 
during  the  period  of  early  hardening,  due  to  the  heat  produced  by 
the  chemical  changes  taking  place,  temperatures  of  from  95°  F.  to 
150°  F.  having  been  observed.1  In  thin  walls  this  is  largely  counter- 
acted by  the  radiation  into  the  atmosphere.  The  influence  of  changes 
of  atmospheric  temperatures  rapidly  decreases  with  the  distance 
from  the  surface  of  the  concrete.  Daily  variations  of  temperature 
are  not  felt  at  depths  of  more  than  2  or  3  feet,  while  seasonal  vari- 
ations may  not  reach  more  than  one-third  the  amount  of  the  change 
in  the  outside  air  at  a  depth  of  10  feet. 

Moisture  Changes. — Variations  in  moisture  conditions  are  of 
greater  importance  than  those  of  temperature  in  causing  mortar  or 
concrete  to  expand  and  contract.  These  changes  are  of  special 
importance  during  the  time  that  the  concrete  is  hardening.  Experi- 
ments indicate  that  concrete  kept  in  dry  air  during  the  period  of 

1  Temperature  Changes  in  Mass  Concrete,  by  Paul  and  Mayhew,  Trans- 
actions, American  Society  of  Civil  Engineers,  Vol.  LXXIX,  1915,  p.  1225. 


134  PLAIN  CONCRETE 

hardening  undergoes  a  progressive  shrinkage,  while  that  kept  in  water 
expands  during  the  same  period,  but  to  a  less  extent.  The  results 
obtained  by  different  investigators  have  varied  considerably  in  the 
extent  of  the  changes  shown.  In  general,  concrete  exposed  to  dry 
air  may  be  expected  to  contract  .04  to  .06  per  cent  of  its  length  in 
six  months  after  mixing,  while  if  kept  under  water  it  may  expand 
.01  to  .02  per  cent.  The  changes  for  cement  mortar  are  greater 
than  for  concrete,  the  extent  of  the  change  being  greater  as  the 
mortar  is  richer. 

Tests  indicate  that  concrete  at  any  age  expands  if  changed  from 
dry  to  wet  condition,  and  contracts  if  changed  from  wet  to  dry. 
Concrete  subject  to  changes  in  moisture  conditions,  therefore,  alter- 
nately expands  and  contracts  with  such  changes,  unless  restrained 
by  its  position  from  such  motion.  We  have  no  means  of  estimating 
the  amount  of  the  variations  to  be  expected  in  concrete  work,  but 
under  ordinary  conditions  these  effects  must  be  much  less  than  the 
progressive  variations  during  hardening. 

Available  data  are  not  sufficient  to  determine  to  what  extent 
the  progressive  expansions  or  contractions  taking  pla?e  during 
hardening  may  be  permanent.1  Indications  are  that  concrete  which 
has  been  kept  wet  during  the  first  month  or  more  and  then  permitted 
to  dry  for  several  months,  does  not  shrink  to  the  same  extent  as  that 
which  is  kept  dry  during  the  whole  period.  Concrete  kept  damp 
during  the  early  period  of  hardening  should  not  crack  when  exposed 
to  the  air  to  the  same  extent  as  that  continuously  dry. 

It  seems  probable  that  under  some  conditions  progressive  changes 
in  dimension  may  take  place  over  a  long  period,  though  it  must 
not  be  inferred  that  work  in  which  the  concrete  is  restrained  from 
such  changes  is  subjected  to  the  stresses  which  would  be  imposed 
by  the  necessity  of  resisting  them  all  at  once.  Concrete  restrained, 
as  in  reinforced  work,  from  yielding  to  the  tendency  to  contract, 
probably  becomes  adjusted  to  the  situation  so  that  it  would  not 
contract  if  the  restraint  were  removed. 

Contraction  joints  are  commonly  used  to  prevent  the  cracking 
of  concrete  by  shrinkage.  The  compressive  strength  of  concrete 
is  usually  sufficient  to  take  up  the  stresses  due  to  expansion  without 
injury  to  the  structure,  but  tensions  due  to  contraction  may  be 
sufficient  to  crack  the  concrete. 

1See,  "Expansion  and  Contraction  of  Concrete  While  Hardening,"  by  A. 
T.  Goldbeck,  Proceedings,  American  Society  for  Testing  Materials,  Vol.  XI, 
p.  563,  also,  "Volume  Changes  in  Portland  Cement  Mortar  and  Concrete,"  by 
A.  H.  White,  Proceedings,  American  Society  for  Testing  Materials,  Vol.  XIV, 
p.  203. 


PLACING  CONCRETE  135 

Thin  concrete  walls  usually  need  contraction  joints  20  to  30  feet 
apart;  in  heavy  walls,  they  may  be  50  or  60  feet  apart.  The  use 
of  light  reinforcement  in  the  exposed  surfaces  between  expansion 
joints  may  prevent  disfiguring  surface  cracks. 

Ordinarily  these  joints  may  be  formed  by  building  the  work  in 
sections  and  allowing  one  section  to  set  before  the  adjoining  one  is 
placed.  This  introduces  planes  of  weakness  through  the  work 
which  will  yield  when  the  wall  contracts.  To  bond  the  ends  together, 
grooves  may  be  left  in  the  sections  first  constructed  and  filled  in 
placing  the  new  work.  Joints  are  sometimes  made  by  inserting 
strips  of  roofing  paper  and  placing  the  new  concrete  against  these, 
or  where  water-tight  work  is  necessary  by  filling  a  thin  opening  in 
the  concrete  with  asphalt  cement. 

86.  Finishing  Concrete  Surfaces. — The  appearance  of  a  con- 
crete structure  depends  largely  upon  the  way  in  which  the  surfaces 
are  finished.  When  the  forms  are  removed,  the  marks  of  the  lumber 
of  the  forms  are  plainly  visible,  and  lines  between  successive  layers 
of  concrete  are  usually  seen.  When  the  concrete  next  the  form  has 
been  carefully  spaded  in  placing  the  concrete,  the  surface  should 
be  fairly  smooth  with  no  vacant  spaces  which  require  filling,  and 
if  the  forms  are  smooth,  a  quite  even,  uniform  appearance  may  be 
obtained.  For  certain  classes  of  structures,  such  as  retaining  walls 
and  bridge  abutments  in  certain  locations,  the  appearance  may  be 
satisfactory  without  further  treatment,  although  the  dead  color  of 
the  smooth  surface  skin  is  not  particularly  pleasing. 

A  smooth  surface  is  sometimes  obtained  by  plastering  with 
cement  mortar — a  method  not  usually  satisfactory,  as  the  mortar 
is  apt  to  scale  off.  A  rough  appearance  is  usually  more  suitable  to 
the  material,  and  the  surface  of  the  concrete  itself  should  be  used. 
When  a  smooth  mortar  surface  is  desired,  it  should  be  obtained  by 
placing  the  mortar  at  the  same  time  as  the  concrete,  which  may  be 
done  by  using  a  movable  form  for  the  mortar.  The  form  slides 
inside  the  main  form  and  separates  the  mortar  from  the  concrete, 
and  is  removed  as  the  materials  are  placed  so  that  they  may  be 
tamped  together. 

A  pleasing  appearance  may  often  be  made  by  scrubbing  the 
surface  with  a  stiff  brush  and  water  as  soon  as  it  has  set  sufficiently 
to  remove  the  forms,  which  removes  the  marks  of  the  forms  and 
brings  the  pieces  of  larger  aggregate  into  view.  Scrubbing  must 
be  done  before  the  concrete  has  hardened  too  much,  usually  within 
twenty-four  hours  of  placing  the  concrete,  and  immediately  after 
removing  the  forms,  as  the  surface  hardens  rapidly  after  the  forms 


136  PLAIN   CONCRETE 

are  taken  off.  In  removing  forms  for  this  purpose,  care  must  be 
used  to  prevent  breaking  the  corners  of  the  concrete,  as,  to  present 
a  good  appearance,  the  edges  must  be  straight  and  sharp.  Scrubbing 
involves  comparatively  little  labor  and  is  an  inexpensive  method 
of  finishing. 

After  the  concrete  surface  is  hard  it  may  be  scrubbed,  and  the 
skin  removed,  by  the  use  of  a  solution  of  about  one  part  hydro- 
chloric acid  to  five  parts  water,  though  this  method  is  quite  laborious 
and  rather  expensive. 

Concrete  surfaces  are  sometimes  finished  by  tooling,  using  the 
axe,  bush-hammer,  or  point.  The  concrete  may  thus  be  made  to 
show  a  very  uniformly  roughened  surface  which  is  very  pleasing. 
If  neatly  done,  this  is  rather  slow  and  expensive,  although  a  roughly 
pointed  effect  may  be  produced  with  less  work. 

The  appearance  of  the  finished  surface  may  be  controlled  by  the 
choice  of  aggregates.  If  a  uniform  appearance  is  desired,  small 
aggregates  may  be  used  on  the  surface.  If  a  more  rough  appearance 
is  wanted,  larger  and  less  uniform  material  may  be  employed.  Pleas- 
ing color  effects  may  often  be  had  by  care  in  the  choice  of  aggregates 
to  be  used  on  the  surface,  or  mortar  colors  may  be  used  for  the  pur- 
pose. White  Portland  cement  may  also  be  used  where  special 
effects  are  desired. 

Breaking  the  continuity  of  a  surface  by  introducing  panels  may 
frequently  improve  its  appearance.  These  are  made  by  nailing 
boards  of  proper  shape  to  the  inside  of  the  forms.  The  surface  may 
be  broken  by  lines  indented  into  the  concrete  by  nailing  strips  of 
triangular  section  to  the  inside  of  the  forms. 

\ 
ART.  23.     WATERTIGHT   CONCRETE 

87.  Permeability  of  Concrete. — The  permeability  of  a  wall  of 
concrete  varies  with  the  size  and  shape  of  the  aggregates,  the  density 
of  the  mixture,  and  the  richness  of  the  mortar.  For  given  aggre- 
gates, the  densest  and  strongest  mixture  will  usually  be  the  least 
permeable,  although  the  least  porous  concrete  is  not  necessarily  the 
least  permeable  when  different  materials  are  used. 

Mortar  composed  of  fine  sand  is  more  porous  and  less  permeable 
than  mortar  of  coarse  sand  mixed  in  the  same  proportions.  Graded 
sand,  with  sufficient  fine  materials,  shows  less  porosity  and  less 
permeability  than  either  fine  or  coarse  sand  alone,  but  with  any  sand, 
the  permeability  of  mortar  decreases  as  the  ratio  of  cement  to  sand 
increases. 


WATERTIGHT  CONCRETE  137 

The  permeability  of  mortar  decreases  with  age  during  the  period 
of  hardening,  and  mortar  subject  to  the  continuous  nitration  of 
water  decreases  in  permeability.  Messrs.  Fuller  and  Thompson  1 
found  that  the  permeability  of  concrete  decreased  as  the  maximum 
size  of  coarse  aggregate  increased,  and  that  gravel  concrete  was  less 
permeable  than  that  made  with  broken  stone. 

The  use  of  sand  cement  (see  Section  16)  in  place  of  Portland 
cement  ordinarily  gives  a  somewhat  more  impervious  concrete,  and 
is  frequently  used  for  the  purpose.  The  extremely  fine  grinding 
to  which  the  cement  is  subjected  in  preparing  the  sand  cement  is 
favorable  to  making  a  water-tight  mortar. 

'Water-proof  Concrete. — With  carefully  selected  and  proportioned 
materials  and  good  workmanship,  concrete  may  be  made  practically 
water-tight.  To  secure  this  result,  rich  mortar  (at  least  1  to  2) 
should  be  used,  and  the  aggregates  graded  to  produce  a  dense  mix- 
ture. The  concrete  should  be  thoroughly  mixed  to  a  plastic  or 
soft,  but  not  too  wet,  consistency,  and  placed  carefully,  eliminating 
joints  if  possible.  When  horizontal  joints  are  unavoidable,  the 
skin .  on  the  old  surface  should  be  broken  and  roughened  before 
placing  the  cement  paste  to  receive  the  new  work.  A  thickness  of 
1  foot  of  well-constructed  concrete  wall  may  be  expected  to  be 
practically  water-tight,  under  a  head  of  50  feet.  No  wall  to  hold 
water  pressure  should  be  less  than  6  inches  thick. 

When  a  lean  concrete  is  used  for  the  body  of  the  work,  a  thin 
surface  of  rich  concrete,  or  of  cement  mortar,  may  be  placed  upon 
the  water  face;  this  face  must  be  built  up  with  the  main  body  of 
the  work  and  firmly  united  with  it,  and  contraction  joints  must  be 
used  where  cracks  are  likely  to  occur. 

Tests  for  Permeability. — The  permeability  of  concrete  is  tested 
by  forcing  water  through  a  block  of  concrete  under  pressure,  the 
block  being  so  arranged  that  the  water  can  escape  only  by  passing 
through  the  concrete.  In  an  apparatus  used  by  Mr.  Thompson  2 
for  this  purpose  the  sides  of  the  mold  were  made  by  two  pieces  of 
wrought  iron  bent  to  a  half-circle  and  bolted  together,  these  rest- 
ing on  a  plank  which  formed  the  bottom  of  the  mold  until  the  con- 
crete had  set.  The  surfaces  of  the  concrete  were  chipped  to  remove 
the  skin,  the  blocks  turned  upside  down  in  making  the  tests,  and 
the  water  measured  which  passed  through  the  block. 

88.  Integral  Waterproofing. — For  the  purpose  of  increasing  the 
water-tightness  of  concrete,  additions  of  other  materials  are  some- 

1  Transactions,  American  Society  of  Civil  Engineers,  Vol.  LIX,  1907,  p.  67. 

2  Proceedings,  American  Society  for  Testing  Materials,  Vol.  VIII,  p.  506. 


138  PLAIN  CONCRETE 

times  made.  There  are  a  number  of  proprietary  compounds  on  the 
market  to  be  mixed  with  the  concrete  to  make  it  impervious,  known 
as  integral  water-proofing  compounds.  Some  of  these  may  be  of 
value,  provided  they  are  not  used  in  lieu  of  proper  proportions  or 
good  work  in  placing  the  concrete,  but  dependence  upon  making 
meager  or  improperly  mixed  concrete  water-tight  by  additions  of 
waterproofing  compounds  is  apt  to  end  in  failure. 

Hydrated  Lime. — The  addition  of  hydrated  lime  to  the  cement 
mortar  used  in  concrete  may  be  useful  in  assisting  in  making  the 
concrete  water-tight.  As  already  noted  (Section  35),  mortar  con- 
taining lime  works  easier,  and  is  preferred  by  masons  for  brickwork 
(Section  60).  A  small  addition  of  hydrated  lime  makes  concrete 
flow  more  readily  in  placing  and  tends  to  prevent  separation  of  the 
materials  in  handling,  and  it  is  sometimes  used  for  this  reason  in 
concrete  which  is  to  be  chuted  to  place. 

Hydrated  lime  may  be  used  in  cement  mortar  to  replace  a  small 
per  cent  by  weight  of  the  cement  without  injury  to  the  strength 
of  the  mortar.  It  is  a  -very  finely  divided  material,  much  more  bulky 
than  the  cement,  and  therefore  renders  the  mortar  less  permeable. 
Where  the  strength  is  sufficient,  a  somewhat  leaner  concrete  may 
be  used  if  hydrated  lime  is  added.  Experiments  by  Mr.  Thompson  1 
show  that  hydrated  lime  may  be  of  considerable  value  in  rendering 
concrete  impervious  under  considerable  heads.  Mr.  Thompson 
recommends  the  addition  of  hydrated  lime  in  the  following  percent- 
ages of  weight  of  dry  hydrated  lime  to  the  weight  of  Portland  cement : 


For  1  part  Portland  cement;    2  parts  sand;    4  parts  stone, 

add  8  per  cent  hydrated  lime. 
For  1  part  Portland  cement;   2f  parts  sand;  4J  parts  stone, 

add  12  per  cent  hydrated  lime. 
For  1  part  Portland  cement;    3  parts  sand;    5  parts  stone, 

add  16  per  cent  hydrated  lime. 

Clay. — Finely  divided  clay  in  the  sand  used  in  making  concrete 
has  been  found  to  lessen  the  permeability  of  the  concrete.  The  clay 
must  be  free  from  vegetable  matter  and  present  in  small  propor- 
tion, not  more  than  5  per  cent  of  the  weight  of  sand.  Finely  pulver- 
ized rock  has  much  the  same  effect.  These  materials  are  of  use 
when  the  mortar  is  lean,  though  for  rich  mortars  they  may  be  detri- 
mental to  strength  without  materially  affecting  the  permeability. 

Alum  and  soap  solution  has  sometimes  been  used  to  mix  with 
the  body  of  concrete  and  seems  to  have  been  fairly  efficient  as  a 

1  Proceedings,  American  Society  for  Testing  Materials,  Vol.  VIII,  p.  500. 


WATERTIGHT  CONCRETE  139 

water-proofing  medium.  In  applying,  it  is  usually  best  to  mix 
powdered  alum  with  the  cement  and  dissolve  the  hard  soap  in  the 
water  to  be  used  in  mixing.  The  soap  may  be  about  3  per  cent  of 
the  weight  of  water,  and  the  alum  about  one-half  the  weight  of  the 
soap. 

Oil-mixed  Concrete. — It  has  been  proposed  to  use  mineral  oil 
as  an  integral  water-proofing.  The  results  of  experiments  by  Mr. 
Page  1  indicated  that  the  use  of  a  small  amount  of  asphaltic  oil  in 
mixing  cement  mortar  decreased  the  permeability  of  the  mortar, 
without  materially  decreasing  its  strength.  He  found  the  crushing 
strength  to  be  somewhat  reduced,  when  the  weight  of  oil  was  10 
per  cent  that  of  the  cement  the  crushing  strength  was  reduced 
about  25  per  cent. 

The  lubricating  effect  of  the  oil  is  such  that  it  cannot  be  used 
for  reinforced  work  with  plain  steel  bars. 

The  oil  recommended  by  Mr.  Page  is  a  fluid  petroleum  resiauai, 
and  he  suggests  the  use  of  5  per  cent  of  the  weight  of  cement  for 
water-proofing  purposes. 

89.  Waterproof  Coatings. — Various  methods  have  been  pro- 
posed and  are  sometimes  used  for  the  treatment  of  concrete  surfaces 
to  make  them  waterproof.  For  ordinary  work,  as  already  stated, 
the  concrete  may  itself  be  made  water-tight  and  nothing  is  needed 
beyond  care  in  the  selection  of  materials  and  in  preparing  and  placing 
the  concrete.  Under  some  circumstances,  however,  as  in  old 
work  or  where  joints  and  cracks  cannot  be  avoided,  it  may  be  neces- 
sary to  provide  some  means  of  protecting  the  surface  of  concrete 
against  the  penetration  of  water. 

Layers  of  Waterproof  Materials. — Probably  the  most  effective 
method  of  protection  is  that  of  applying  layers  of  waterproof  paper 
or  felt  coated  with  asphalt  or  coal-tar  pitch.  The  concrete  is  first 
coated  with  hot  asphalt,  layers  of  paper  or  felt  are  then  placed,  and 
each  coated  with  the  hot  asphalt,  the  applications  being  made  from 
3-ply  to  6-ply,  depending  upon  the  degree  of  protection  needed — a 
method  frequently  employed  on  subways,  and  bridge  floors  with 
good  results.  Objection  has  been  made  to  this  method  on  account 
of  it  preventing  the  radiation  of  heat  in  subway  work.  Careful 
workmanship  is  necessary  in  placing  such  a  protection;  the  layers 
must  break  joints  properly,  and  be  protected  against  being  punctured 
after  being  placed. 

Cement  Grout. — Washing  the  surface  of  concrete  with  a  grout  of 

1  Oil-Mixed  Portland  Cement  Concrete,  Bulletin  No.  46,  Office  of  Public 
Roads,  Washington. 


140  PLAIN  CONCRETE 

neat  Portland  cement  may  sometimes  be  of  use  on  a  surface  exposed 
to  water,  serving  to  fill  voids  and  cracks  which  may  exist  in  the 
surface. 

Plastering  with  cement  mortar,  or  other  materials  mixed  with 
cement,  is  sometimes  adopted  as  a  means  of  waterproofing.  Usually 
such  plastering  needs  protection  against  possible  weather  cracks, 
and  sometimes  the  plaster  does  not  adhere.  On  horizontal  or  inclined 
surfaces  a  troweled  mortar  finish,  similar  to  that  commonly  used 
on  sidewalks,  makes  a  water-tight  job,  provided  care  be  taken  to 
guard  against  cracks,  and  to  insure  the  bonding  of  the  mortar  to 
the  concrete. 

Alum  and  Soap. — A  solution  of  soap  and  alum  is  often  used  to 
wash  the  surface  of  concrete;  it  is  of  the  same  character  as  the  mix- 
ture employed  in  integral  waterproofing,  and  is  also  sometimes  used 
for  mixing  with  cement  mortar  for  plastering  the  surface. 

Bituminous  coatings  consisting  of  one  or  more  coatings  of  asphalt 
or  tar  painted  on  hot  are  sometimes  employed,  such  applications 
being  often  used  on  the  outside  of  the  cellar  walls  of  buildings.  A 
number  of  proprietary  compounds  are  available  for  use  as  surface 
washes,  some  of  which  seem  quite  effective,  though  in  many  cases 
they  require  renewal  from  time  to  time.  Some  interesting  tests 
of  a  number  of  methods  of  waterproofing  concrete  surfaces  were 
made  by  Mr.  F.  M.  McCullough,  and  the  results  given  in  Bulletin 
No.  336  of  the  University  of  Wisconsin,  on  "  Tests  of  the  Permea- 
bility of  Concrete," 

ART.    24.  DURABILITY  OF   CONCRETE 

90.  Destructive  Agencies. — Well-constructed  concrete,  under  the 
conditions  usually  met  in  ordinary  work,  is  practically  an  inde- 
structible material,  but  under  special  conditions,  when  subject  to 
the  action  of  agencies  peculiar  to  particular  classes  of  work,  con- 
crete may  yield  like  any  other  material.  The  cracking  of  concrete 
through  contraction,  as  explained  in  Section  85,  may  be  of  injury 
to  a  structure,  but  the  body  of  concrete  itself  is  not  destroyed 
or  disintegrated  by  cracking. 

Concrete  has  sometimes  seemed  to  be  injured  by  the  action  of 
certain  chemical  agencies,  such  as  oils,  salts  of  sea  water,  alkalies, 
and  acids.  Destruction  by  electrolysis  and  by  fire  have  also  some- 
times occurred. 

Effect  of  Oils. — Mineral  oils  have  no  ill  effects  upon  concrete, 
and  have  sometimes  been  used  for  the  purpose  of  rendering  the 


DURABILITY  OF  CONCRETE  141 

surface  less  pervious,  and  to  prevent  dust  upon  surfaces  subject  to 
abrasion.  Some  animal  fats  and  vegetable  oils  seem  to  cause  dis- 
integration in  concrete.  When  such  oils  at  high  temperatures  come 
into  contact  with  concrete,  a  combination  of  lime  from  the  cement 
with  acids  contained  in  the  oils  produces  compounds  which  expand 
when  crystallizing  in  the  pores.  In  manufacturing  plants,  where 
animal  or  vegetable  oil  may  come  into  contact  with  concrete,  the 
effect  of  such  contact  should  be  carefully  investigated. 

Effect  of  Acids. — Water  containing  acids  should  not  come  into 
contact  with  concrete  before  it  has  well  hardened.  Hard  concrete 
may  resist  the  action  of  such  solutions  unless  they  are  in  rather 
concentrated  form.  The  effect  of  any  destructive  agency  of  this 
character  wih1  be  much  greater  for  porous  concrete  into  which  the 
liquid  may  readily  penetrate  than  for  dense  concrete. 

Electrolysis. — In  some  instances,  injury  to  concrete  containing 
steel  reinforcement  has  resulted  from  the  leakage  of  electric  cur- 
rents through  the  mass.  The  Joint  Committee  on  Concrete  in  its 
1917  report  make  the  following  statements  concerning  electrolysis: 

Electrolysis. — The  experimental  data  available  on  this  subject  seem  to  show 
that  while  reinforced  concrete  structures  may,  under  certain  conditions,  be  injured 
by  the  flow  of  electric  current  in  either  direction  between  the  reinforcing  material 
and  the  concrete,  such  injury  is  generally  to  be  expected  only  where  voltages  are 
considerably  higher  than  those  which  usually  occur  in  concrete  structures  in 
practice.  If  the  iron  be  positive,  trouble  may  manifest  itself  by  corrosion  of  the 
iron  accompanied  by  cracking  of  the  concrete,  and,  if  the  iron  be  negative,  there 
may  be  a  softening  of  the  concrete  near  the  surface  of  the  iron,  resulting  in  a 
destruction  of  the  bond.  The  former,  or  anode  effect,  decreases  much  more 
rapidly  than  the  voltage,  and  almost  if  not  quite  disappears  at  voltages  that  are 
most  likely  to  be  encountered  in  practice.  The  cathode  effect,  on  the  other  hand, 
takes  place  even  under  very  low  voltages,  and  is  therefore  more  important  from 
a  practical  standpoint  than  that  of  the  anode. 

Structures  containing  salt  or  calcium  chloride,  even  in  very  small  quantities, 
are  very  much  more  susceptible  to  the  effects  of  electric  currents  than  normal 
concrete,  the  anode  effect  progressing  much  more  rapidly  in  the  presence  of 
chlorine,  and  the  cathode  effect  being  greatly  increased  by  the  presence  of  an 
alkali  metal. 

There  is  great  weight  of  evidence  to  show  that  normal  reinforced  concrete 
structures  free  from  salt  are  in  very  little  danger  under  most  practical  conditions, 
while  non-reinforced  concrete  structures  are  practically  immune  from  electrolysis 
troubles. 

91.  Effect  of  Sea  Water  upon  Concrete. — There  have  been 
numerous  instances  of  failure  of  concrete  subject  to  the  action  of 
sea  water,  the  causes  of  which  are  not  fully  determined.  The  results 
of  experiments  seem  to  indicate  that  salts  contained  in  sea  water 
act  upon  nearly  all  cements  to  which  the  water  has  free  access, 


142  PLAIN  CONCRETE 

producing  compounds  which  expand,  disrupting  the  mass  of  mortar, 
or  which  soften  the  mortar  and  cause  disintegration.  This  action 
is  probably  due  to  sulphates  in  the  sea  water,  which  are  decomposed 
in  contact  with  the  free  lime  of  the  cement,  the  sulphuric  acid  com- 
bining with  the  lime.  A  considerable  deposit  of  magnesia  also 
commonly  occurs  in  cement  mortar  when  exposed  to  sea  water,1 
indicating  that  the  sulphate  of  magnesia  may  be  the  source  of  the 
trouble. 

Those  cements  which  contain  the  most  lime  are  usually  most 
affected  by  the  action  of  sea  water.  Cements  containing  consider- 
able alumina  should  not  be  used  for  work  in  sea  water,  siliceous 
cements,  or  those  in  which  alumina  is  replaced  by  iron  oxide  being 
preferable.  In  France  a  siliceous  hydraulic  lime  known  as  lime  of 
teil  is  extensively  used  for  such  work. 

The  addition  of  finely  ground  puzzolanic  materials  to  Portland 
cement  has  been  found  useful  in  preventing  the  disintegrating  effects 
of  sea  water.  These  materials  probably  combine  with  and  reduce 
the  amounts  of  free  lime  available  for  combination  with  the  sea 
salts.  As  used,  they  also  render  the  mortar  less  permeable. 

Mortars  of  fine  sand  are  found  to  be  more  affected  by  sea  water 
than  those  of  coarse  or  graded  sands. 

The  injurious  action  of  sea  water  is  dependent  upon  the  water 
having  access  to  the  body  of  the  concrete,  hence  it  is  important  in 
such  work  to  use  concrete  of  maximum  density,  or  to  protect  the 
body  of  the  concrete  by  a  surface  of  dense  mortar  or  concrete.  The 
Joint  Committee  on  Concrete  in  its  1917  report  makes  the  following 
reference  to  work  in  sea  water: 

The  data  available  concerning  the  effect  of  sea  water  on  concrete  or  reinforced 
concrete  are  limited  and  inconclusive.  Sea  walls  out  of  the  range  of  frost  action 
have  been  standing  for  many  years  without  apparent  injury.  In  many  places 
serious  disintegration  has  taken  place.  This  has  occurred  chiefly  between  low 
and  high  tide  levels  and  is  due,  evidently,  in  part  to  frost  Chemical  action  also 
appears  to  be  indicated  by  the  softening  of  the  mortar.  To  effect  the  best  resist- 
ance to  sea  water,  the  concrete  must  be  proportioned,  mixed  and  placed  so  as 
to  prevent  the  penetration  of  sea  water  into  the  mass  or  through  the  joints.  The 
aggregates  should  be  carefully  selected,  graded  and  proportioned  with  the  cement 
so  as  to  secure  the  maximum  possible  density;  the  concrete  should  be  thoroughly 
mixed;  the  joints  between  old  and  new  work  should  be  made  watertight;  and 
the  concrete  should  be  kept  from  exposure  to  sea  water  until  it  is  thoroughly 
hard  and  impervious. 

1  Alexandre,  Annales  des  Fonts  et  Chaussees,  1890,  Vol.  I,  p.  408.  Candlot, 
Ciment  et  Chaux  Hydraulique,  Paris,  1891.  Feret,  Annales  des  Fonts  et  Chaussees, 
1892,  Vol.  II,  p.  93. 


DURABILITY  OF  CONCRETE  143 

92.  Effect  of  Alkalies. — In  some  localities  in  the  arid  regions 
of  the  Western  States  difficulty  has  been  met  in  the  use  of  concrete 
because   of   the   disintegrating    effects   of   alkaline   waters — effects 
similar  to  those  of  sea  water  and  probably  due  to  the  same  causes. 
The  most  serious  disintegration  is  found  where  the  concrete  is  alter- 
nately wet  and  dry,  although  in  some  cases  the  whole  of  the  concrete 
below  water  has  been  affected. 

On  many  irrigation  projects  large  quantities  of  concrete  are  being 
used,  and  the  problem  of  dealing  with  the  alkaline  salts,  with  which 
the  soil  is  impregnated  in  some  localities,  has  become  a  serious  one. 
These  alkaline  deposits  vary  in  character  in  different  places,  com- 
prising salts  of  potassium,  sodium,  calcium,  and  magnesium.  The 
ill  effects  seem  to  occur  where  sulphates  are  present  in  considerable 
quantities,1  which  agrees  with  the  results  of  studies  of  the  action 
of  sea  water.  The  same  precautions  may  be  taken  in  selection  of 
materials  as  for  work  in  sea  water,  but  all  cements  seem  to  be  affected 
to  some  extent  by  contact  with  these  salts.  The  use  of  dense  con- 
crete, or  the  application  of  protective  coatings  to  prevent  access  of 
the  alkaline  water  to  the  interior  of  the  mass  of  concrete,  offers 
the  best  means  of  preventing  disintegration. 

93.  Resistance  to  Fire. — Experience  indicates  that  concrete,  when 
properly  used,  is  one  of  the  best  materials  for  resisting  fire.     The 
surface  of  concrete  immediately  exposed  to  the  fire  is  injured  and 
may  become  dehydrated,  but  concrete  is  a  poor  conductor  of  heat, 
and  the  penetration  of  the  dehydrating  effect  is  extremely  slow. 
Experiments  by  Professor  Woolson2  show  that  when  a  mass  of 
concrete  is  subjected  to  high  heat  for  several  hours,  the  temperature 
1  inch  beneath  the  surface  is  several  hundred  degrees  below  that 
at  the  surface.     With  the  temperature  of  1500°  F.  at  the  surface 
for  two  hours,  the  temperature  at  2  inches  beneath  the  surface  was 
from  500°  to  700°  F.,  and  at  3  inches  beneath  the  surface  about 
200  to  250°  F. 

When  concrete  is  used  as  structural  material,  where  it  is  liable 
to  be  subjected  to  serious  fire  risk,  a  layer  of  concrete  next  the  exposed 
surface  should  be  considered  as  fireproofing  and  not  included  in  the 
section  necessary  for  resisting  stresses. 

The  Joint  Committee  in  its  report  of  1917  discusses  fireproofing 
as  follows : 

Concrete,  because  incombustible  and  of  a  low  rate  of  heat  conductivity,  is 

XJ.  Y.  Jewett,  Proceedings  American  Society  for  Testing  Materials,  Vol. 
VIII,  1908,  p.  484. 

2  Proceedings,  American  Society  for  Testing  Materials,  Vol.  VII,  1907,  p.  408. 


144  PLAIN  CONCRETE 

highly  efficient  and  admirably  adapted  for  fire-proofing  purposes.  This  has  been 
demonstrated  by  experience  and  tests. 

The  dehydration  of  concrete  probably  begins  at  about  500°  F.  and  is  completed 
at  about  900°  F.,  but  experience  indicates  that  the  volatilization  of  the  water 
absorbs  heat  from  the  surrounding  mass,  which,  together  with  the  resistance  of 
the  air  cells,  tends  to  increase  the  heat  resistance  of  the  concrete,  so  that  the 
process  of  dehydration  is  very  much  retarded.  The  concrete  that  is  actually 
affected  by  fire  and  remains  in  position  affords  protection  to  that  beneath  it. 

The  thickness  of  the  protective  coating  should  be  governed  by  the  intensity 
and  duration  of  a  possible  fire  and  the  rate  of  heat  conductivity  of  the  concrete. 
The  question  of  the  rate  of  heat  conductivity  of  concrete  is  one  which  requires 
further  study  and  investigation  before  a  definite  rate  for  different  classes  of  con- 
crete can  be  fully  established.  However,  for  ordinary  conditions  it  is  recom- 
mended that  the  metal  be  protected  by  a  minimum  of  2  inches  of  concrete  on 
girders  and  columns,  1£  inches  on  beams,  and  1  inch  on  floor  slabs. 

Where  fireproofing  is  required  and  not  otherwise  provided  in  monolithic 
concrete  columns,  it  is  recommended  that  the  concrete  to  a  depth  of  1|  inches 
be  considered  as  protective  covering  and  not  included  in  the  effective  section. 

The  corners  of  columns,  girders,  and  beams  should  be  beveled  or  rounded, 
as  a  sharp  corner  is  more  seriously  affected  by  fire  than  a  round  one;  experience 
shows  that  round  columns  are  more  fire  resistive  than  square. 

ART.  25.     STRENGTH   OF  PLAIN   CONCRETE 

94.  Compressive  Strength. — There  are  several  variables  which 
affect  the  strength  of  concrete.  The  quality  and  quantity  of  cement, 
the  kind  of  aggregates  and  their  grading,  the  proportions  of  fine 
to  coarse  aggregate,  the  thoroughness  of  mixing,  the  consistency, 
the  degree  of  compacting,  and  the  conditions  under  which  hardening 
takes  place,  all  have  an  influence  upon  the  strength  of  the  resulting 
concrete. 

Thorough  mixing  and  careful  placing  and  compacting  of  the 
concrete  should  be  obtained  in  all  work.  Carelessness  always  reduces 
its  strength,  and  is  wasteful  and  unnecessary. 

The  Joint  Committee  on  Concrete  recommends  that  the  materials 
be  proportioned  to  secure  as  nearly  as  possible  a  maximum  density. 
"  The  fine  and  coarse  aggregates  should  be  used  in  such  proportions 
as  will  secure  maximum  density.  These  proportions  should  be  care- 
fully determined  by  density  experiments  and  the  grading  of  the  fine 
and  coarse  aggregates  should  be  uniformly  maintained,  or  the  por- 
portions  changed  to  meet  the  varying  sizes."  They  also  recommend 
that  "  the  materials  be  mixed  wet  enough  to  produce  a  concrete 
of  such  consistency  as  will  flow  sluggishly  into  the  forms,  and  about 
the  metal  reinforcement  when  used,  and  which,  at  the  same  time, 
can  be  conveyed  from  the  mixer  to  the  forms  without  separation 
of  the  coarse  aggregate  from  the  mortar." 


STRENGTH  OF  PLAIN  CONCRETE  145 

For  such  concrete,  the  Committee  suggests  the  following  values 
of  ultimate  strength  in  compression  as  those  which  should  be  obtained 
for  the  materials  and  proportions  listed,  the  ratios  given  being  those 
of  cement  to  the  volumes  of  fine  and  coarse  aggregates  measured 
separately.  This  ultimate  strength  is  that  developed  at  an  age  of 
twenty-eight  days,  in  cylinders  8  inches  in  diameter  and  16  inches 
long  of  the  consistency  described  above,  made  and  stored  under 
laboratory  conditions. 

TABLE  OF  COMPRESSIVE  STRENGTHS  OF  DIFFERENT  MIXTURES  OF  CONCRETE 

(In  Pounds  per  Square  Inch) 

Aggregate.  1:3  1  :  4|  1:6  1  :  7|  1:9 

Granite,  trap  rock 3300  2800  2200  1800  1400 

Gravel,    hard    limestone    and    hard 

sandstone 3000  2500  2000  1600  1300 

Soft  limestone  and  sandstone 2200  1800  1500  1200  1000 

Cinders 800          700  600  500  400 

BEARING 

When  compression  is  applied  to  a  surface  of  concrete  of  at  least  twice  the 
loaded  area,  a  stress  of  35  per  cent  of  the  compressive  strength  may  be  allowed 
in  the  area  actually  under  load. 

AXIAL   COMPRESSION 

For  concentric  compression  on  a  plain  concrete  pier,  the  length  of  which 
does  not  exceed  4  diameters,  or  on  a  column  reinforced  with  longitudinal  bars 
only,  the  length  of  which  does  not  exceed  12  diameters,  22.5  per  cent  of  the 
compressive  strength  may  be  allowed. 

Allowable  stresses  for  concrete  in  reinforced  work  are  given  in 
Chapter  VI. 

Cement. — The  strength  of  concrete  varies  neany  .in  proportion 
to  the  cement  contained  by  it,  and  the  ratio  of  cement  to  aggregate 
should  be  selected  to  give  the  strength  needed  in  the  particular 
work  in  hand. 

The  Committee  suggests: 

For  reinforced  concrete  construction,  one  part  cement  to  a  total  of  six  parts 
of  fine  and  coarse  aggregates  measured  separately  should  generally  be  used. 
For  columns,  richer  mixtures  are  preferable.  In  massive  masonry  or  rubble 
concrete  a  mixture  of  1  :  9  or  even  1:12  may  be  used. 

These  proportions  should  be  determined  by  the  strength  or  other  qualities 
required  in  the  construction  at  the  critical  period  of  use.  Experience  and  judg- 
ment based  on  observation  and  tests  of  similar  conditions  in  similar  localities 
are  excellent  guides  as  to  the  proper  proportions  for  any  particular  case. 


146  PLAIN  CONCRETE 

Size  of  Aggregate. — The  values  given  above  are  suggested  for 
concrete  as  used  in  reinforced  work  and  correspond  to  materials 
broken  to  rather  small  maximum  sizes.  Stones  of  larger  maximum 
dimensions  ordinarily  show  somewhat  higher  strengths.  A  stone 
broken  to  2j-inch  maximum  size  will  sometimes  show  strength  20 
to  35  per  cent  higher  than  the  same  stone  broken  to  1-inch  maximum 
size,  if  both  be  properly  graded. 

Consistency. — The  mushy  consistency  recommended  in  the  report 
of  the  Committee  is  most  convenient  for  ordinary  use  in  concrete 
work,  particularly  in  reinforced  work.  In  massive  work,  a  stiffer 
plastic  consistency  gives  a  slightly  higher  strength  if  the  concrete 
is  properly  compacted  in  placing.  The  strength  rapidly  decreases 
as  the  quantity  of  water  is  made  greater,  so  that  the  materials  begin 
to  separate  and  considerable  laitance  forms. 

Strength  is  gained  more  slowly  by  concrete  mixed  wet  than  by 
that  mixed  with  less  water.  A  stiff  plastic  concrete  may  have  con- 
siderable more  strength  at  seven  days  than  a  wetter  mushy  concrete 
though  the  difference  will  have  largely  disappeared  in  twenty-eight 
days. 

Growth  in  Strength. — It  is  customary  to  use  tne  strength  at  twenty- 
eight  days  in  fixing  the  stresses  to  be  allowed  on  concrete  in  struc- 
tures. This  strength  would  usually  be  attained  before  maximum 
loads  could  be  applied.  The  strength  of  concrete  under  normal 
conditions  continues  to  increase  through  a  considerable  period. 
Tests  have  shown  that  average  concrete  may  be  expected  to  reach 
about  twice  the  twenty-eight-day  strength  in  two  or  three  years 
if  kept  from  becoming  too  dry.  Specimens  kept  dry  show  a  con- 
siderably smaller  increase,  and  may  ultimately  gain  but  little  more 
than  the  twenty-eight-day  strength. 

Grading  of  Aggregates. — With  the  same  ratio  of  cement  to  total 
aggregates,  the  strength  of  concrete  is  greater  when  the  aggregates 
are  graded  to  give  more  dense  mixtures.  The  amount  of  cement 
required  to  give  a  definite  strength  is  less  for  well-graded  aggregates 
than  for  those  giving  more  porous  concrete.  In  some  instances 
it  is  possible,  by  sifting  the  aggregates  into  several  sizes  and  recombin- 
ing  in  proper  proportions,  to  reduce  considerably  the  quantity  of 
cement  necessary  to  reach  the  required  density  and  strength,  with 
a  material  saving  in  cost.  In  one  case,  with  a  poorly  graded  stone, 
it  was  found  that  if  the  stone  be  sifted  into  three  sizes  and  recombined, 
1  :  2J  :  6  concrete  of  the  graded  stone  gave  as  much  strength  as 
1:2:4  concrete  of  the  ungraded  material.  The  saving  in  cost  of 
cement  amounted  to  80  cents  per  cubic  yard,  with  an  estimated 


STRENGTH  OF  PLAIN  CONCRETE  147 

additional  cost  of  mixing  of  about  20  cents.  Such  results  are  obtained 
only  for  material  which  is  badly  graded  originally,  and  probably  for 
average  materials  the  saving  in  cost  of  cement  would  not  be  enough 
to  pay  for  regrading.  On  any  important  work,  however,  it  is  worth 
while  to  examine  carefully  the  materials  with  reference  to  their 
granulometric  composition. 

95.  Tests  for  Compressive  Strength. — The  compressive  strength 
of  concrete  has  commonly  been  tested  on  6-inch  or  12-inch  cubes, 
and  much  of  the  available  data  is  based  upon  such  tests.  The  desir- 
ability of  eliminating  the  corners  has  led  to  the  use  of  cylindrical 
specimens,  which  are  found  much  easier  to  make  and  handle  satis- 
factorily. The  use  of  a  test  piece  whose  height  is  greater  than  its 
lateral  diameter  is  also  found  advantageous.  Blocks  of  concrete 
under  crushing  loads  usually  yield  through  shearing  on  surfaces 
making  angles  of  about  60°  with  the  horizontal,  and  by  using  blocks 
whose  heights  are  twice  the  diameter  sufficient  freedom  is  allowed 
for  such  action.  Tests  have  seemed  to  indicate  that  the  strength 
of  blocks  varies  somewhat  with  the  ratio  of  height  to  diameter,  cubes 
showing  25  to  35  per  cent  more  strength  per  square  inch  than  cylin- 
ders whose  heights  are  twice  their  diameters.  Blocks  of  greater 
relative  height  show  a  further  loss  of  strength,  but  to  much  less 
degree,  those  having  a  height  five  tunes  the  diameter  giving  an 
average  strength  about  90  per  cent  of  those  with  a  ratio  of  2  to  1. 

A  Committee  of  the  American  Concrete  Institute  recommended  1 
that  a  cylindrical  test  piece  be  used,  whose  height  is  twice  the 
diameter,  and  diameter  at  least  four  times  the  maximum  size  of  the 
aggregate.  Cylinders  8  inches  in  diameter  and  16  inches  high  are 
used  as  standard  by  the  Joint  Committee  on  Concrete,  though 
cylinders  6  inches  by  12  inches  are  also  sometimes  used. 

Forms  made  of  cast  iron,  with  a  metal  base,  machined  smooth 
and  true,  are  made  by  manufacturers  of  testing  apparatus;  they 
are  somewhat  expensive,  but  are  far  more  satisfactory  in  use  than 
lighter  forms.  Forms  made  of  sheet  metal  with  flanges  to  bolt  or 
clamp  together  may  be  used  without  the  metal  base  by  placing  them 
on  plate  glass. 

Sampling  the  materials  should  be  carefully  done  to  insure  obtain- 
ing fair  samples  for  the  tests.  To  secure  an  average  sample,  the 
method  of  quartering  is  sometimes  applied,  which  consists  in  taking 
shovelfuls  of  material  from  different  parts  of  the  pile,  mixing  them 
together  and  spreading  out  on  the  mixing  surface.  The  resulting 
layer  of  material  is  then  divided  into  quarters,  two  opposite  quarters 
1  Journal,  American  Concrete  Institute,  Oct.,  1914. 


148  PLAIN  CONCRETE 

are  shoveled  away,  the  other  two  quarters  are  mixed  again  and  the 
operation  repeated  until  a  sample  of  the  size  desired  is  obtained. 
When  the  materials  are  not  uniform  and  vary  in  different  parts  of 
the  supply,  it  may  be  desirable  to  take  separate  samples  from  each 
part  and  make  comparative  tests. 

Measurement  of  materials  should  be  by  weight  in  making  tests. 
When  the  proportions  used  in  work  are  by  volume  the  volume- 
weight  of  the  materials  should  first  be  ascertained,  and  the  weight 
proportions  for  the  test  pieces  determined  accordingly. 

Mixing  should  be  done  on  an  impervious  surface.  The  cement 
and  sand  should  first  be  mixed  thoroughly,  to  a  uniform  color,  and 
spread  evenly  on  the  mixing  surface.  The  coarse  aggregate  should 
then  be  spread  over  the  dry  mixture  of  sand  and  cement  and  the 
whole  turned  several  times  dry.  Water  may  then  be  added  in  a 
crater  and  the  mass  turned  and  wet  until  it  is  thoroughly  worked 
to  uniform  consistency. 

On  important  work,  it  may  often  be  desirable  to  test  the  con- 
crete as  it  is  being  used,  by  making  test  pieces  from  the  concrete  as 
delivered  for  placing  in  the  work. 

Forming  the  Block. — The  concrete  should  be  tamped  into  the  forms 
in  layers  so  as  to  bring  the  mortar  to  the  surfaces  and  leave  no  open 
spaces  around  the  edges.  After  the  concrete  has  set,  the  top  of  the 
block  may  be  smoothed  by  leveling  with  cement  paste  or  mortar, 
or  with  plaster  of  Paris,  and  a  piece  of  glass  pressed  down  on  top 
and  left  until  the  mortar  has  set. 

Storage. — In  making  tests  for  purposes  of  comparison,  the  test 
pieces  should  be  kept  moist  while  they  are  hardening.  Blocks  left 
in  dry  air  do  not  gain  strength  normally. 

Testing. — In  making  the  tests,  spherical  bearing  blocks  should 
be  used  and  care  taken  to  permit  the  adjustment  of  the  test  pieces 
to  uniform  bearing,  properly  centered. 

96.  Tensile  and  Transverse  Strength. — There  are  very  few  data 
available  concerning  the  tensile  strength  of  concrete,  as  it  is  not  used 
where  it  is  subject  to  direct  tension,  and  this  strength  is  of  com- 
paratively little  interest.  The  tensile  strength  is  called  into  play 
in  unreinforced  beams,  but  the  action  is  quite  different  from  that 
of  a  direct  pull.  The  results  of  tests  indicate  that  the  tensile  strength 
of  concrete  commonly  varies  from  about  one-fifteenth  to  one-twelfth 
of  the  compressive  strength. 

The  transverse  strength  is  dependent  upon  the  tensile  resistance 
of  the  material,  and  plain  concrete  is  therefore  a  weak  material  for 
use -in  beams.  On  account  of  this  weakness,  concrete  is  seldom  used 


COST  OF  CONCRETE  WORK  149 

for  beams  without  reinforcement,  and  in  the  computation  of  reinforced 
beams,  the  resistance  of  the  concrete  on  the  tension  side  of  the  beam 
is  neglected. 

The  few  data  available  indicate  that  the  modulus  of  rupture  for 
plain  concrete  beams  varies  from  about  one-eighth  to  one-fifth  of 
the  compressive  unit  strength,  or  that  it  is  approximately  twice  the 
strength  in  direct  tension.  These  values  are  based  upon  the  appli- 
cation of  the  common  theory  of  flexure,  and  the  usual  formulas  for 
homogeneous  materials.  The  difference  between  the  modulus  of 
rupture  and  tensile  strength  may  be  partly  accounted  for  by  the  fact 
that  the  modulus  of  elasticity  is  not  constant  and  the  neutral  axis 
does  not  remain  at  the  gravity  axis,  but  changes  in  position,  approach- 
ing the  compression  side  of  the  beam  as  the  load  increases,  so  that 
the  actual  tension  does  not  reach  the  computed  modulus  of  rupture. 

ART.  26.     COST   OF   CONCRETE  WORK 

97.  Cost  of  Materials. — The  cost  of  cement  varies  with  the 
demand,  and  for  different  localities,  with  the  cost  of  transportation. 
Prices  for  cement  delivered  should  always  be  obtained  in  making 
estimates  for  work.  The  cost  of  wagon  transportation  in  delivery 
of  cement  to  the  work  varies  with  the  condition  of  the  roads  and 
the  means  of  transport  available.  A  team  may  haul  10  or  12  barrels 
of  cement  on  a  fair  country  road,  and  travel  about  20  miles  per  day; 
on  hard-surface  roads  the  loads  may  be  increased,  and  auto  trans- 
portation over  good  roads  is  less  expensive. 

The  approximate  quantities  of  materials  required  may  be  taken 
from  the  tables  in  Section  77.  The  following  figures  represent 
costs  of  work  previous  to  the  World  War.  The  unsettled  prices 
since  existing  make  it  impracticable  to  give  later  data  of  any  value. 
These  costs  should  probably  be  doubled  at  present  (spring,  1920). 

Sand. — For  ordinary  work  in  urban  communities,  sand  may 
usually  be  purchased  delivered,  and  estimates  should  be  based  upon 
the  local  prices,  which  vary  in  different  localities  (about  $.70  to  $1.60 
is  common)  according  to  the  nearness  of  the  source  of  supply  and  the 
way  in  which  the  sand  is  delivered. 

When  sand  is  purchased  by  the  ton,  the  weight  per  cubic 
yard  must  be  ascertained  to  figure  the  cost  accurately.  Ordinary 
screened  sand,  with  about  45  per  cent  voids,  weighs  from  2400  to 
2500  pounds  per  cubic  yard. 

For  sand  taken  from  a  pit,  the  costs  include  digging  the  sand, 
loading  into  wagons,  and  hauling  to  the  work.  In  digging  and  load- 


150  PLAIN  CONCRETE 

ing,  1  to  1J  hours  labor  is  ordinarily  required  per  cubic  yard  and 
at  20  cents  per  hour  the  cost  may  be  from  25  to  35  cents  per  cubic 
yard.  On  well-organized  work,  where  hauling  is  continuous,  hauling 
may  cost  7  to  10  cents  per  1000  feet  of  distance,  while  on  smaller 
and  less  well-arranged  work,  the  cost  may  reach  12  to  15  cents, 
with  team  and  driver  at  $5  per  day,  but  decreases  as  the  length  of 
haul  increases.  Hand  screening  usually  costs  somewhat  less  than 
loading,  perhaps  from  15  to  25  cents  per  cubic  yard. 

Stone  and  Gravel. — Broken  stone  or  gravel,  like  sand,  may  usually 
be  purchased  for  ordinary  work  by  the  cubic  yard  or  by  the  ton. 
The  weight  per  cubic  yard  depends  upon  the  specific  gravity  of  the 
stone  and  the  percentage  of  voids.  For  ordinary  crusher-run  stone 
with  the  chips  removed  and  about  45  per  cent  voids,  granite  or  hard 
limestone  weighs  about  2500  pounds  per  cubic  yard,  trap  about 
2700  pounds;  stone  containing  more  fine  material,  in  which  the  voids 
are  40  per  cent,  weighs  about  10  per  cent  more  than  these  figures. 

When  gravel  is  to  be  obtained  from  a  pit,  the  cost  of  digging  and 
loading,  with  labor  at  20  cents  an  hour,  commonly  varies  from  about 
35  to  50  cents  per  cubic  yard,  according  to  the  quantity  required 
and  the  arrangements  for  loading,  while  hauling  is  about  the  same 
as  for  sand.  The  cost  of  screening  gravel  by  hand  may  vary  from 
30  to  55  cents  per  cubic  yard,  45  cents  being  an  ordinary  average. 

Average  Costs. — Under  average  conditions,  with  a  moderate  haul 
the  price  of  sand  delivered  on  work  varies  from  about  90  cents  to 
$1.20  per  cubic  yard;  similarly  screened  gravel,  $1.20  to  $1.50,  and 
broken  stone,  $1.40  to  $1.75.  When  gravel  or  broken  stone 
is  delivered  on  cars,  about  15  cents  per  cubic  yard  must  be  allowed 
for  unloading. 

98.  Cost  of  Labor. — The  labor  required  in  concrete  work  includes 
handling  the  materials  to  the  mixing  platform,  mixing  the  concrete 
and  handling  the  concrete  to  place.  The  cost  varies  with  the  organiz- 
ation of  the  work  and  the  experience  of  the  men.  The  ability  of 
the  foreman  to  systematize  and  control  the  work  is  one  of  the  most 
important  items.  The  author  on  one  occasion  had  two  almost 
identical  pieces  of  work  in  progress  at  the  same  time,  and  found 
after  the  first  few  days  that  one  job  was  costing  about  40  per  cent 
more  than  the  other,  due  almost  entirely  to  differences  in  the  manage- 
ment of  the  foremen. 

When  materials  are  conveniently  arranged  and  the  concrete, 
after  mixing,  may  be  shoveled  into  place  from  the  mixing  platform, 
the  cost  of  mixing  and  placing  concrete  is  commonly  from  $0.90  to 
$1.25  per  cubic  yard,  with  labor  at  20  cents  per  hour.  Wheeling 


COST  OF  CONCRETE  WORK  151 

the  concrete  to  place  costs  about  15  cents  per  cubic  yard  for  the  first 
50  feet  and  5  cents  for  each  additional  50  feet.  For  work  of  moder- 
ate size  the  cost  of  machine  mixing  does  not  differ  very  materially 
from  hand  mixing,  when  the  overhead  charges  are  included. 

In  placing  mass  concrete  in  large  work,  the  labor  costs  may  be 
materially  reduced  where  machinery  is  used  for  mixing  and  handling 
the  concrete.  Costs  from  60  to  75  cents  per  cubic  yard  are  not 
uncommon. 

In  reinforced  concrete  structural  work,  the  placing  of  concrete 
is  more  expensive  than  ordinary  work  mentioned  above,  and  the 
labor  cost  of  mixing  and  placing  concrete  may  be  from  $1.50  to  $2 
per  cubic  yard — figures  which  will  vary  with  the  difficulty  of  spading 
and  compacting  in  the  forms, ;  and  with  the  means  of  distribution 
over  the  work.  ' 

In  work  for  which  considerable  machinery  is  required,  a  charge 
for  use  of  plant  and  supplies  must  be  included,  which  will  vary  with 
the  size  of  the  job  and  the  extent  of  the  plant  required.  For  build- 
ing operations  where  a  hoisting  plant  is  necessary,  it  will  be  from 
60  cents  to  $1  per  cubic  yard. 

99.  Total  Costs. — The  costs  for  concrete  in  place  include  the 
costs  for  materials,  labor,  and  plant.  In  the  construction  of  a 
1:3:6  concrete  foundation  for  street  pavement,  an  average  cost 
is  approximately  as  follows: 

Cement,  1.02  barrel  at  $1.75 $1 . 79 

Sand,  0.46  cubic  yard  at  $1.00 1 ...   0.46 

Stone,  0.92  cubic  yard  at  $1.40 1 .29 

Labor,  per  cubic  yard 1 . 10 


Total  cost  per  cubic  yard $4 . 64 

For  the  construction  of  a  concrete  building,  an  average  cost 
for  1  :  2  :  4  concrete  of  crusher  run  stone  (45  per  cent  voids)  may 
be  as  follows: 

Cement,  1.47  barrel  at  $1.80 $2.65 

Sand,  0.43  cubic  yard  at  $1 0.43 

Stone,  0.87  cubic  yard  at  $1.60 1.39 

Labor  per  cubic  yard 1 . 50 

Plant  per  cubic  yard 0 . 80 

Total  cost  per  cubic  yard $6 . 77 

Allowance  should  be  made  for  waste  of  materials,  which  always 
occurs  to  some  extent — in  some  cases  5  per  cent  of  the  amount  of 


152  PLAIN  CONCRETE 

materials  necessary  to  form  the  required  concrete  is  needed  to  cover 
this  loss.  Care  in  handling  the  materials  and  close  supervision  of 
the  mixing  may  reduce  the  loss  to  a  negligible  quantity,  where  the 
work  is  concentrated  in  large  units. 

The  above  figures  do  not  include  the  cost  of  forms  or  of  steel 
for  reinforcement.  Forms  must  be  specially  designed  for  each 
structure  and  the  cost  varies  widely.  In  massive  construction  or 
in  foundation  work,  the  forms  may  be  a  comparatively  small  item, 
while  for  heavy  walls  requiring  support  on  the  sides,  they  may  cost 
$.50  per  cubic  yard  or  less.  On  structural  work,  including  beams 
and  columns,  the  cost  of  forms  is  frequently  greater  than  that  of 
the  concrete.  In  such  cases,  only  a  careful  design  for  the  forms, 
and  estimate  of  the  materials  and  labor  required  for  their  erection, 
can  give  accurate  data  as  to  cost.  In  building  work,  the  cost  of 
forms  is  sometimes  roughly  estimated  as  about  8  to  10  cents  per 
square  foot  of  surface  of  concrete,  where  the  use  of  the  materials 
may  be  repeated,  and  when  the  forms  can  be  used  but  once  the  cost 
is  much  greater. 

Valuable  information  concerning  the  cost  of  concrete  construction 
may  be  found  in  "  Concrete  Costs  "  by  Taylor  and  Thompson,  and 
in  "  Concrete  Construction  "  by  Gillette  and  Hill. 

"Concrete,  Plain  and  Reinforced,"  by  Taylor  and  Thompson,  gives 
a  very  complete  discussion  of  the  materials,  proportions,  methods 
of  mixing  and  placing,  and  properties  of  plain  concrete. 


CHAPTER  VI 
REINFORCED   CONCRETE 

ART.   27.     GENERAL  PRINCIPLES 

100.  Object  of  Reinforcement. — Concrete  and  steel  are  frequently 
combined  in  structural  work  in  two  distinct  types  of  construction: 

.1.  Structural  Members  of  Steel  Encased  in  Concrete. — In  this  type 
of  construction,  the  steel  member  is  designed  to  carry  the  loads, 
and  the  concrete  is  used  for  protection  of  the  steel  against  the 
weather  or  fire,  or  sometimes  to  give  lateral  stiffness  to  the  member. 

2.  Reinforced  concrete,  in  which  the  load-carrying  member  is 
made  of  concrete,  the  steel  being  used  to  strengthen  the  concrete 
by  taking  stresses  that  the  concrete  is  unfitted  to  resist. 

Structures  of  the  first  type,  in  which  the  concrete  is  used  to  give 
stiffness  to  the  structure,  are  often  classed  as  reinforced  concrete, 
although  reliance  is  placed  upon  the  steel  alone  for  carrying  the 
loads.  These  are  not,  however,  designed  in  accordance  with  the 
theories  of  reinforced  concrete. 

The  advantages  to  be  gained  by  combining  steel  and  concrete 
are  due  to  the  fact  that  concrete  is  extremely  weak  and  uneconomical 
when  subjected  to  tension,  but  has  much  greater  strength  and  is  a 
convenient  and  economical  material  for  resistance  to  compressions, 
while  steel  must  be  made  of  special  forms  satisfactorily  to  carry 
compression,  but  may  be  used  for  resisting  tension  in  the  form  of 
ordinary  bars. 

In  structural  forms,  such  as  beams,  in  which  both  tensile  and 
compressive  stresses  are  developed,  the  combination  of  the  two 
materials  offers  an  economical  means  of  construction  when  the  con- 
ditions are  favorable,  and  the  use  of  this  type  of  construction  has 
been  rapidly  extending  during  the  past  few  years. 

In  the  use  of  concrete  and  steel  in  combination,  the  following 
properties  of  the  materials  are  important: 

1.  When  steel  bars  are  imbedded  in  concrete,  the  concrete 
adheres  to  the  steel  and  develops  a  considerable  bond  strength, 
which  may  be  relied  upon  to  make  the  two  materials  act  together. 

153 


154  REINFORCED  CONCRETE 

2.  Concrete  acts  as  a  protection  to  the  steel  against  rust.     In 
a  number  of  instances  in  removing  concrete  structures,  it  has  been 
found  that  the  steel,  after  being  embedded  for  several  years,  was  in 
good  condition  and  free  from  rust.     To  form  an  efficient  protection 
the  concrete  must  be  mixed  rather  wet,  so  that  the  steel  is  completely 
covered  with  a  coating  of  mortar. 

3.  The  coefficients  of  expansion  for  the  two  materials  are  so 
nearly  the  same  that  no  stresses  need  be  considered  as  resulting 
from  differences  of  expansions  or  contractions  due  to  changes  in 
temperature. 

4.  Changes  in  dimension  occur  in  unreinforced  concrete  during 
hardening  (see  Section  85)  and  with  variations  in  moisture  condi- 
tions.    When  these  changes  are  restrained  by  reinforcement,  the 
concrete  seems  to  adjust  itself  to  the  situation,  adopting  permanently 
the  form  in  which  it  is  held,  without  being  placed  under  appreciable 
stress. 

101.  Bond  Strength. — The  stresses  carried  by  the  steel  in  a 
reinforced  concrete  structural  member  must  usually  be  trans- 
mitted to  the  steel  through  the  bond  between  the  steel  and  concrete. 
Tests  and  experience  show  that  plain  steel  bars  imbedded  in 
concrete  develop  considerable  bond  strength  which  may  be  relied 
upon  to  hold  the  bars  permanently  in  place  in  resisting  stresses 
which  tend  to  separate  them  from  the  concrete.  Experiments  upon 
the  adhesion  of  plain  bars  to  concrete  show  that  the  bond  strength 
is  approximately  proportional  to  the  area  of  surface  contact,  and 
varies  with  the  quality  of  the  concrete,  being  nearly  proportional 
to  the  strength  in  compression. 

When  tests  are  made  by  pulling  a  bar  of  steel  out  of  a  block  of 
concrete  in  which  its  end  has  been  embedded,  the  compression  of 
the  concrete  may  influence  the  results,  and  the  bond  strength  shown 
be  greater  than  would  be  developed  in  a  beam  where  both  steel  and 
concrete  are  under  tension.  When  the  length  of  the  bar  embedded 
in  the  concrete  is  considerable,  the  bar  may  begin  to  slip  at  the  sur- 
face of  the  block  before  the  resistance  of  the  more  deeply  embedded 
part  is  fully  brought  into  play,  and  the  bond  resistance  per  unit 
of  surface  area  be  less  than  for  shorter  lengths.  In  tests  at  the 
University  of  Wisconsin  no  differences  in  unit  bond  strengths  was 
found  between  6-inch  and  12-inch  embedments. 

Various  tests  have  shown  ultimate  bond  strengths  for  ordinary 
concrete  from  about  200  to  700  pounds  per  square  inch  of  surface 
area  of  bar.  In  general,  for  concrete  as  commonly  employed  in 


GENERAL  PRINCIPLES  155 

structural  work  the  unit  bond  resistance  for  plain  bars  may  be  from 
200  to  300  pounds  per  square  inch. 

Twisted  and  deformed  bars  are  made  in  a  number  of  forms  for 
the  purpose  of  increasing  the  bond  strength,  and  are  extensively 
used  in  reinforced  concrete  work;  their  raised  projections  or  uneven 
surfaces  give  a  mechanical  bond  and  carry  considerable  more  load 
before  finally  yielding  than  plain  bars,  although  initial  slip  may 
occur  under  about  the  same  stresses. 

102.  Reinforcing  Steel. — The  Joint  Committee  on  Concrete 
makes  the  following  recommendations 1  concerning  steel  for  reinforce- 
ment bars: 

The  Committee  recommends  as  a  suitable  material  for  reinforcement,  steel 
of  structural  grade  filling  the  requirements  of  the  Specifications  for  Billet-Steel 
Concrete  Reinforcement  Bars  of  the  American  Society  for  Testing  Materials. 

For  reinforcing  slabs,  small  beams  or  minor  details,  or  for  reinforcing  for 
shrinkage  and  temperature  stresses,  steel  wire,  expanded  metal,  or  other  reticu- 
lated steel  may  be  used,  with  the  unit  stresses  hereinafter  recommended. 

The  reinforcement  should  be  free  from  flaking  rust,  scale  or  coatings  of  any 
character  which  would  tend  to  reduce  or  destroy  the  bond. 

The  Specifications  of  the  American  Society  for  Testing  Materials 
are  given  in  their  Book  of  Standards  or  may  be  obtained  in  reprints 
from  the  Secretary  of  the  Society. 

On  important  work,  it  is  common  to  purchase  steel  subject  to 
these  specifications,  and  to  submit  steel  to  careful  inspection  at 
the  mills. 

Engineers  differ  as  to  the  advisability  of  using  "  hard-grade  " 
steel  for  reinforcement.  As  a  concrete  beam  usually  gives  way 
when  the  yield  point  of  the  steel  is  reached,  through  the  cracking 
and  crushing  of  the  concrete,  the  yield  point  may  be  considered 
as  the  ultimate  strength  for  concrete  work,  and  some  engineers 
prefer  to  use  hard-grade  steel  on  account  of  its  high  yield  point. 
Medium  steel  is,  however,  usually  preferred  as  less  expensive  and 
less  likely  to  be  brittle.  When  hard-grade  steel  is  used,  either  high 
carbon  or  cold  deformed  material,  it  should  be  carefully  tested,  as 
it  is  more  variable  in  quality  than  medium  steel,  but  when  meeting 
the  specifications  is  a  superior  material. 

For  ordinary  reinforced  concrete  work,  mild  steel  as  commonly 
found  upon  the  market  is  usually  employed.  It  is  desirable  to 
subject  this  to  the  cold  bending  test,  which  is  the  most  important 

1  Proceedings,  American  Society  of  Civil  Engineers,  Dec.  1916. 


156  REINFORCED  CONCRETE 

test  for  reinforcing  steel,  and  upon  failure  the  material  should 
always  be  rejected. 

103.  Ratio  of  Moduli  of  Elasticity. — The  modulus  of  elasticity 
of  a  material  is  the  ratio  of  unit  stress  to  the  corresponding  unit 
deformation,  within  the  elastic  limit  of  the  material. 

When  two  materials  with  different  moduli  of  elasticity,  like  steel 
and  concrete,  are  combined  in  a  structural  member  so  that  they 
must  act  together,  as  in  a  column,  they  will  each  be  extended  or 
compressed  to  the  same  amount,  and  the  unit  stress  carried  by  each 
material  will  be  proportional  to  the  modulus  of  elasticity  of  the 
material. 

When  a  beam  is  loaded  so  as  to  cause  it  to  bend,  it  is  lengthened 
on  the  convex  and  shortened  on  the  concave  side.  Tests  of  reinforced 
concrete  beams  show  that  any  plane  section  of  the  beam  before 
bending  remains  approximately  plane  when  bent,  and  that  the 
amount  of  extension  or  shortening  is  proportional  to  the  distance 
from  its  neutral  surface.  In  such  beams  the  stresses  upon  steel 
and  concrete  at  the  same  distance  from  the  neutral  surface  are  pro- 
portional to  the  moduli  of  elasticity  of  the  materials. 

In  the  discussion  of  stresses  in  any  structural  member  of  steel 
and  concrete  subject  to  deformation,  it  is  therefore  necessary  to 
know  the  ratio  of  the  moduli  of  elasticity  of  the  two  materials  in 
order  to  determine  the  amount  of  stress  carried  by  each. 

The  modulus  of  elasticity  of  steel  is  practically  the  same  for  the 
different  grades  and  is  independent  of  the  ultimate  strength  or  yield 
point.  An  average  value  is  about  30,000,000  lb./in.,  and  this  value 
is  usually  employed  in  reinforced  concrete  computations. 

The  modulus  of  elasticity  of  concrete  is  not  a  constant,  but 
varies  with  the  stress,  becoming  less  as  the  stress  becomes  greater. 
For  small  stresses,  within  the  limits  of  allowable  working  stress, 
however,  the  variation  is  very  small,  and  the  modulus  of  elasticity 
may  be  taken  as  constant  without  appreciable  error.  The  formulas 
in  common  use  are  based  upon  the  assumption  of  a  constant  modulus 
of  elasticity,  and  variation  of  stress  in  beam  design  proportional 
to  distance  from  the  neutral  axis. 

Tests  for  the  determination  of  the  moduli  of  elasticity  of  con- 
cretes vary  considerably  in  results,  and  indicate  that  the  modulus 
depends  upon  the  quality  of  the  concrete,  being  approximately 
proportional  to  the  compressive  strength.  The  modulus  also  varies 
with  the  age  of  the  concrete,  increasing  with  age  more  rapidly  than 
does  the  strength  of  the  concrete. 


GENERAL  PRINCIPLES  157 

The  Joint  Committee  makes  the  following  recommendation 1 
concerning  the  modulus  of  elasticity: 

The  value  of  the  modulus  of  elasticity  of  concrete  has  a  wide  range,  depending 
on  the  materials  used,  the  age,  the  range  of  stresses  between  which  it  is  considered, 
as  well  as  other  conditions.  It  is  recommended  that  in  computations  for  the 
position  of  the  neutral  axis,  and  for  the  resisting  moment  of  beams  and  for  com- 
pression of  concrete  in  columns,  it  be  assumed  as: 

(a)  One-fortieth  that  of  steel,  when  the  strength  of  the  concrete  is  taken 

as  not  more  than  800  pounds  per  square  inch. 
(6)  One-fifteenth  that  of  steel,  when  the  strength  of  the  concrete  is  taken 

as  greater  than  800  pounds  per  square  inch  and  less  than  2200 

pounds  per  square  inch. 

(c)  One-twelfth  that  of  steel,  when  the  strength  of  the  concrete  is  taken 

as  greater  than  2200  pounds  per  square  inch  and  less  than  2900 
pounds  per  square  inch  and 

(d)  One-tenth  that  of  steel,  when  the  strength  01  the  concrete  is  taken 

as  greater  than  2900  pounds  per  square  inch. 

Although  not  rigorously  accurate,  these  assumptions  will  give  safe  results. 
For  the  deflection  of  beams  which  are  free  to  move  longitudinally  at  the  supports, 
in  using  formulas  for  deflection  which  do  not  take  into  account  the  tensile 
strength  developed  in  the  concrete,  a  modulus  of  one-eighth  of  that  of  steel  is 
recommended. 

104.  Reinforced  Concrete  in  Tension. — When  reinforced  con- 
crete is  subjected  to  tensile  stresses,  the  two  materials  act  together, 
each  carrying  unit  stresses  in  proportion  to  its  modulus  of  elasticity, 
so  long  as  the  stresses  do  not  exceed  the  strength  of  the  concrete. 
When,  however,  the  steel  is  stressed  to  a  fair  working  load,  the 
stress  upon  the  concrete  will  have  passed  its  breaking  strength, 
and  it  can  no  longer  be  considered  as  carrying  stress — a  condition 
which  usually  exists  in  reinforced  concrete  beams  when  carrying 
normal  working  loads.  The  steel  in  such  beams  is  designed  to  carry 
all  the  tensions,  the  concrete  on  the  tension  side  merely  holding  the 
steel  in  place. 

In  the  earlier  studies  of  reinforced  beams,  it  was  supposed  that 
the  concrete  when  reinforced  became  capable  of  carrying  greater 
tensions  than  plain  concrete,  and  beam  formulas  were  proposed  in 
which  it  was  assumed  that  the  concrete  carried  part  of  the  tension. 
Later  investigations,  however,  showed  that  this  was  erroneous  and 
these  formulas  are  no  longer  used  in  design. 

Observations  upon  beams  under  tests  have  shown  that  minute 
cracks,  invisible  to  the  naked  eye,  frequently  exist  in  the  concrete 
1  Proceedings,  American  Society  of  Civil  Engineers,  Dec.,  1916. 


158  REINFORCED  CONCRETE 

surface  on  the  tension  side  while  the  beam  is  carrying  only  a  safe 
load — a  discovery  made  in  testing  damp  beams  with  the  tension 
side  uppermost  at  the  University  of  Wisconsin.  Dark,  wet  lines 
appeared  upon  the  surface  at  about  the  time  that  the  ultimate 
strength  of  the  concrete  was  reached,  and  these  later  developed  into 
fine  cracks.  Experience  with  this  type  of  construction  indicates 
that,  when  the  materials  are  properly  used,  no  injury  results  from 
this  overstressing  of  the  concrete,  and  that  the  steel  is  fully  pro- 
tected by  the  concrete. 

ART.  28.     RECTANGULAR  BEAMS  WITH  TENSION  REINFORCEMENT 

105.  Flexure  Formulas. — The  common  or  straight-line  formulas 
for  reinforced  concrete  beams  are  based  upon  the  ordinary  theory 
of  flexure,  and  involve  the  following  assumptions: 

(1)  A  section  of  the  beam  that  is  plane  before  bending  remains 
plane  when  bent. 

(2)  The  modulus  of  elasticity  of  concrete  is  constant  within 
the  limits  of  safe  unit  stresses. 

(3)  The  concrete  resists  compression  only,   all  tensions   being 
carried  by  the  steel. 

(4)  Initial  stresses  due  to  expansion  or  contraction  of  the  con- 
crete are  negligible. 

These  assumptions  greatly  simplify  the  computations  and  are 
found  experimentally  to  be  sufficiently  accurate  within  the  limits 
of  stresses  used  in  ordinary  beam  design;  they  are  not  applicable 
to  ultimate  loads  and  can  be  used  only  for  working  loads  and  work- 
ing stresses. 

The  following  notation  will  be  used : 

h  =  total  depth  of  beam; 

6  =  breadth  of  beam; 

d= depth  of  center  of  gravity  of  steel  below  compression  face 

of  beam,  or  effective  depth  of  beam; 

kd  =  depth  of  neutral  axis  below  compression  face  of  beam; 
jd= distance  between  centers  of  tension  and  compression; 
A  =  area  of  cross-section  of  steel; 

p  =  ratio  of  steel  area  to  effective  area  of  beam  (p  =  A/bd)\ 
/s  =  unit  tensile  stress  on  steel; 

/c  =  unit  compressive  stress  on  concrete  at  compression  face; 
Es  =  modulus  of  elasticity  of  steel; 
EC  =  modulus  of  elasticity  of  concrete; 


RECTANGULAR  BEAMS  WITH  TENSION  REINFORCEMENTS     159 


n  =  ratio  of  moduli,  ES/EC; 
C  =  total  compression  in  concrete; 
T  =  total  tension  in  steel; 
M= resisting  moment  or  bending  moment. 


Ikd, 


FIG.  45. — Reinforced  Concrete  Beam. 

Assuming  that  a  plane  section  before  bending  remains  plane 
after  bending,  we  have  (see  Fig.  45), 

fc/Ee       kd 
f,/E,    d-kd' 


or 


from  which  we  obtain 


or 


nfe_    k 
fc~l-k' 

fs_n(l-k) 

fc          k      ' 

nfc 


fs+nfc 


(1) 


The  total  compression  on  the  concrete  is,  C  =  %fckbd. 
The  total  tension  on  the  steel  is,  T=Afs=fspbd.    These  are  equal 
for  equilibrium;  equating  and  reducing, 


or 


fs==k_ 
fc    2p 


(2) 


160  REINFORCED  CONCRETE 

Combining  (1)  and  (2)  we  have 


and  solving  for  k, 


=     2pn+(pn)2-pn.       .     .     .     (4) 


The  centroid  of  compressive  stresses  is  at  a  distance  kd/3  from 
the  compressive  face  of  the  beam,  and 

jd  =  d-kd/3, 
or 


From  the  foregoing  it  is  readily  seen  that  the  ratio  of  the  unit 
stresses  on  the  steel  and  concrete,  and  the  values  of  &,  j  and  p  are 
interdependent.  If  the  unit  stresses  and  value  of  n  be  assumed, 
k  and  the  required  percentage  of  steel  may  be  found  from  Formulas 
(1)  and  (2).  If  the  percentage  of  steel  be  known  and  the  ratio  n 
assumed,  the  values  of  k  and  the  ratio  fs/fc  may  be  found  from  (4) 
and  (2). 

The  resisting  moment  of  the  beam  is  due  to  the  couple  formed 
by  the  tensions  and  compressions  and  is  equal  to  either  of  them  into 
the  arm  of  the  couple  : 

M=Tjd=Afsjd=fspjbd2,      ......     (6) 

or 

M  =  Cjd  =  ±fckjbd2,       ........     (7) 

and 


Formulas  (6)  and  (7)  give  a  means  of  determining  the  moment 
of  resistance  of  a  beam  of  known  dimensions  and  safe  unit  stresses, 
while  from  (8)  the  necessary  dimensions  may  be  found  to  resist  any 
given  bending  moment  with  assumed  unit  stresses  in  steel  and  con- 
crete. 

Examples.  —  The  problems  arising  in  the  use  of  these  formulas 
are  of  two  kinds  —  the  design  of  beams  to  carry  certain  loads;  the 
investigation  of  existing  beams  to  determine  the  loads  they  may 
safely  carry,  or  the  unit  stresses  resulting  from  given  loads.  The 
following  examples  illustrate  the  use  of  the  formulas  for  these  pur- 
poses : 

1.  A  reinforced  concrete  beam  is  to  carry  a  bending  moment  of 
152,000  in.-lb.  The  safe  unit  stresses  upon  concrete  and  steel  are 


RECTANGULAR  BEAMS  WITH  TENSION  REINFORCEMENTS      161 

600  and  14,000  lb./in.2  respectively.     ft  =15.     Find  dimensions  for 
the  beam  and  area  of  steel  required. 
Solution.  —  Formula  (1)  gives 


from  (5) 


15X600 
14000+15X600 


(8)  now  gives 

152000  _ 

"  14000  X.  0084  X.  87" 

We  may  now  assume  a  value  for  either  b  or  d,  or  fix  a  relation  be- 
tween them.  Assuming  6  =  8  inches,  we  have  Sd2  =  1490  and  d  =  13.7 
inches.  A  =  pbd=  .0084  X  8  X  13.7  =  .92  in.2  Taking  d  as  13  f  inches, 
if  the  concrete  extends  If  inches  below  the  steel,  the  total  depth, 
7i=13f+lf  =  15i  inches. 

2.  A  concrete  beam  is  9  inches  wide  and  16  inches  deep,  and  is 
reinforced  with  four  J-inch  round  steel  bars,  with  centers  2  inches 
above  the  lower  surface  of  the  beam.  The  safe  unit  stresses  for  the 
concrete  and  steel  are  700  and  14,000  lb./in.2  respectively.  n=15. 
What  is  the  safe  bending  moment  for  the  beam? 

Solution—  The   area  of  steel  is  A  =  .4418X4  =  1.767  in.2,   and 

A     1.767 
P  =  fcT9 
Using  (4), 


=  \/2X!5X.014+(15X.014)2-15X.014 


This  shows  that  if  a  stress  of  14,000  lb/in.2  be  brought  upon  the 
steel,  the  stress  upon  the  concrete  will  be  greater  than  700  lb./in.2 
Hence  the  safe  moment  is  that  which  causes  a  stress  of  700  lb./in.2 
in  the  concrete,  or  applying  (7) 

M  =  ~(.47  X  .84  X  9  X  14)2  =  243750  in.-lb. 

z 

3.  If  the  beam  in  the  preceding  example  is  subjected  to  a  bend- 
ing moment  of  225,000  in.-lb.,  what  are  the  maximum  stresses  upon 
the  steel  and  concrete? 

Solution.  —  As  in  the  preceding  case,  we  find  A  =  1.767  in.2, 
A;  =  .47,  ,/  =  0.84  and  fs/fc=  16.8. 


162  REINFORCED  CONCRETE 

From  (6) 

-      *  225°°°        =10810. 


Ajd     1.  767  X.  84X14 
fe=  10810/16.8  =  644  lb./in.2 

106.  Tables.  —  The  labor  of  computation  in  the  use  of  the  above 
formulas  may  be  considerably  lessened  by  tabulation  of  values  of 
some  of  the  terms  involved. 

In  Formula  (8),  the  denominators  fspj  and  %fckj  are  constant 
for  any  particular  values  of  fa  and  fc,  and  may  be  represented  by 
a  single  term, 


Substituting  this  in  (8)  we  have 

M  =  Rbd?, 
or 

bd2  =  M/R  .........     (9) 

In  Table  VII  values  of  j,  k,  p  and  R  are  given  for  several  values 
of  fs  and  fc  when  n  =  15. 

Table  VIII  gives  values  of  the  same  quantities  when  n=  12. 

In  Table  IX  values  of  fs/fc,  k,  j  and  %jk  are  given  for  various 
values  of  p,  with  n=  12  and  n=  15. 

Table  X  gives  the  areas  and  weights  of  square  and  round  steel 
bars  of  the  sizes  commonly  used  in  reinforced  concrete  work. 

Examples.  —  The  use  of  the  tables  will  be  illustrated  by  solving  a 
few  problems. 

(4)  A  reinforced  concrete  beam  is  to  resist  a  bending  moment  of 
315,000  in.-lb.  The  safe  unit  stresses  upon  the  concrete  and  steel 
are  650  and  16,000  lb./in.2  respectively.  n=15.  Find  dimensions 
for  the  beam  and  area  of  steel  required. 

Solution.—  From  Table  VII,  for  /,=  16,000  and  /c  =  650,  we  find 
72=108  and  p  =  .0078.  Substituting  this  value  of  R  in  (9),  bd?  = 
M/R  =  315000/108  =  2917.  If  we  assume  6  =  10  inches,  we  have 
d2  =  2917/10  =  291.7  and  d=l7  inches. 

If  the  center  of  the  steel  be  2  inches  from  the  surface  of  the  con- 
crete, the  total  depth  of  the  beam,  h=  17+2  =  19  inches. 

The  area  of  steel  required,  A  =  pbd  =  .0078  X  10  X  17  =  1.33  in.2 

Example  5.  —  A  concrete  beam  is  10  inches  wide  and  18  inches  deep 
and  is  reinforced  with  four  f-inch  round  steel  bars,  with  centers  2 
inches  above  the  lower  surface  of  beam.  The  safe  unit  stresses  for 


RECTANGULAR  BEAMS  WITH  TENSION  REINFORCEMENTS     163 


p 

o 

?2 


00 

i—i   CO   *O 

^    00   O 


CO 

O 


iO 

CO 


O5    1>    CO 

iO     Tfl     i—  1 
Tt<     00     O 


C^l     rH 

IO    rH 

OOO 


OO 

CO 


OO 


CM    CO   CO 

CO     TJH     rH 

•<*  oo  o 


oo 

(M    rH 
1C    TH 

00   0 


<N 

co 


O 
CO   r-  I   CM 


t^   O 

10     rH 

00   O 


CO 

<N 


- 

iO   i—  i 

oo  o 


CO    OO 


OS 


CO   00   O  CO   00 

'a 


IO 

COOSiO 
CO  OO  CO 
COOOO 


O   t^   !>•  TJH 

CO    00    O  .CO 


00  00 


8  S3 


<M  10 

Oi    '^    CO  CO   Oi    *O 


g 


164 


REINFORCED  CONCRETE 


concrete  and  steel  are  700  and  16,000  lb./in.2  respectively,     n  =15. 
What  is  the  safe  bending  moment  for  the  beam? 

Solution. — From  Table  X,  four  f-inch  round  bars  have  area  of 
1.77  in.2  and  p=  1.77/160  =  . 0116.  From  Table  IX,  for  p  =  .0116 
and  n=15,  we  find  /s//c=19.2  and  jfc/2  =  188. 


TABLE    VIII.—  RECTANGULAR    BEAMS    WITH    TENSION 
REINFORCEMENT 


=  12 


fs 

fc—  LBS./IN.  2. 

700 

750 

800 

850 

900 

950 

1000 

15,000 

k 

.359 

.375 

.390 

.405 

.419 

.432 

.444 

3 

.880 

.875 

.870 

.865 

.860 

.856 

.852 

P 

.0084 

.0094 

.0104 

.0115 

.0125 

.0136 

.0147 

R 

111. 

123. 

136. 

149. 

162. 

175. 

189. 

16,000 

k 

.344 

.360 

.375 

.389 

.403 

.416 

.429 

j 

.885 

.880 

.875 

.870 

.866 

.861    .857 

P 

.0075 

.0084 

.0094 

.0104 

.0114 

.0123 

.0134 

R 

107. 

119. 

131. 

144. 

157. 

170. 

184. 

18,000 

k 

.318 

.333 

.348 

.362 

.375 

.388 

.409 

j 

.894 

.889 

.884 

.879 

.875 

.871 

.867 

P 

.0062 

.0070 

.0078 

.0086 

.0094 

.0103 

.0111 

R 

100. 

111. 

123. 

135. 

148. 

161. 

174. 

20,000 

k 

.296 

.310 

.324 

.338 

.351 

.363 

.375 

j 

.901 

.897 

.892 

.887 

.883 

.879 

.875 

P 

.0052 

.0058 

.0065 

.0072 

.0079 

.0086 

.0094 

R 

93. 

104. 

116. 

128. 

140. 

152. 

164. 

When  /.=  16,000,  fc=  16,000/19.2  =  833  lb./in.2  This  is  greater 
than  the  allowable  stress  on  concrete,  and  the  safe  bending  moment 
is  that  which  causes  a  stress  of  700  lb./in.2  on  the  concrete,  or  by 
(7)  700 X. 188X10X16X16  =  336,900  in.-lb. 

Example  6. — A  concrete  beam  9  inches  wide  and  15  inches  deep  is 
reinforced  with  five  J-inch  round  bars  of  steel,  with  centers  2  inches 
above  lower  face  of  beam.  The  beam  carries  a  bending  moment  of 
185,000  in.-lb.  If  n=  12,  find  the  unit  stresses  on  the  steel  and  con- 
crete. 


RECTANGULAR  BEAMS  WITH  TENSION  REINFORCEMENTS      165 


TABLE    IX.— RECTANGULAR    BEAMS    WITH    TENSION 
REINFORCEMENT 


p 

n  =  12 

n  =  15 

ft 

j 

jk/2 

fs/fc 

R/fs 

ft 

3 

jk/2 

fs/fc 

R/fs 

.0015 

.173 

.942 

.081 

57.7 

.0014 

.191 

.936 

.089 

63.7 

.0014 

.002 

.196 

.935 

.092 

49.0 

.0019 

.217 

.928 

.101 

54.3 

.0019 

.0025 

.217 

.928 

.100 

43.4 

.0023 

.239 

.920 

.110 

47.8 

.0023 

.003 

.235 

.922 

.108 

39.3 

.0027 

.258 

.914 

.118 

43.0 

.0027 

.0035 

.251 

.916 

.115 

35.8 

.0032 

.276 

.908 

.125 

39.4 

.0032 

.004 

.266 

.911 

.121 

33.3 

.0037 

.292 

.903 

.132 

36.3 

.0036 

.0045 

.279 

.907 

.126 

31.0 

.0041 

.307 

.898 

.137 

33.9 

.0040 

.005 

.291 

.903 

.131 

29.1 

.0045 

.320 

.893 

.142 

31.6 

.0045 

.0055 

.303 

.899 

.136 

27.6 

.0049 

.332 

.889 

.147 

30.2 

.0049 

.006 

.314 

.895 

.141 

26.7 

.0054 

.344 

.885 

.152 

28.7 

.0053 

.0065 

.325 

.892 

.145 

24.9 

.0058 

.355 

.882 

.156 

27.5 

.0057 

.007 

.334 

.889 

.149 

23.9 

.0062 

.365 

.878 

.160 

26.1 

.0061 

.0075 

.344 

.885 

.153 

23.0 

.0066 

.375 

.875 

.164 

25.0 

.0066 

.008 

.353 

.882 

.156 

22.1 

.0071 

.384 

.872 

.167 

24.0 

.0070 

.0085 

.361 

.879 

.159 

21.3 

.0075 

.393 

.869 

.171 

23.1 

.0074 

.009 

.369 

.877 

.162 

20.5 

.0079 

.402 

.866 

.174 

22.3 

.0078 

.0095 

.377 

.874 

.165 

19.8 

.0083 

.410 

.863 

.177 

21.6 

.0082 

.0100 

.384 

.872 

.167 

19.2 

.0087 

.418 

.861 

.180 

21.0 

.0086 

.011 

.398 

.867 

.175 

18.1 

.0095 

.433 

.856 

.185 

19.7 

.0094 

.012 

.412 

.863 

.178 

17.2 

.0103 

.446 

.851 

.190 

18.6 

.0102 

.013 

.425 

.859 

.182 

16.4 

.0111 

.458 

.847 

.194 

17.7 

.0110 

.014 

.436 

.855 

.186 

15.6 

.0120 

.470 

.843 

.198 

16.9 

.0118 

.015 

.447 

.851 

.190 

14.9 

.0128 

.482 

.839 

.202 

16.1 

.0126 

.016 

.457 

.848 

.194 

14.3 

.0136 

.493 

.836 

.206 

15.4 

.0134 

.017 

.467 

.845 

.197 

13.7 

.0144 

.503 

.832 

.210 

14.8 

.0142 

.018 

.476 

.842 

.200 

13.2 

.0152 

.513 

.829 

.213 

14.3 

.0149 

.019 

.485 

.839 

.203 

12.8 

.0159 

.522 

.826 

.216 

13.8 

.0157 

.020 

.493 

.836 

.206 

12.4 

.0167 

.531 

.823 

.219 

13.3 

.0165 

From  Table  X,  five  ^-inch  round  bars  have  an  area  of  .98  in.2, 
and  p  =  A/bd  =  .  98/117  =  .  0084.     From  Table  IX,  for  P=.0084  and 
n  =  12,  we  have  jk/2  =  .158  and  fs/fc  =  21.5.     By  Formula  (7), 
M  185000 


e  =  21.5X770=  16550  lb./in.2 


166 


REINFORCED  CONCRETE 


TABLE  X.— STEEL  BARS.     AREAS  AND  WEIGHTS 


Diam. 
in 
Inches. 

Weight 
per  Ft. 
Pounds. 

Perm- 
eter 
Inches. 

AREAS  OF  DIFFERENT  NUMBERS  OF  BARS  —  SQUARE  INCHES. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

SQUARE  BARS. 

1/4 

0.212 

1.00 

0.0625 

0.12 

0.19 

0.25 

0.31 

0.38 

0.44 

0.50 

0.56 

5/16 

0.333 

1.25 

0.0977 

0.20 

0.29 

0.39 

0.49 

0.59 

0.68 

0.78 

0.88 

3/8 

0.478 

1.50 

0.1406 

0.28 

0.42 

0.56 

0.70 

0.84 

0.98 

1.12 

1.27 

7/16 

0.671 

1.75 

0.1914 

0.38 

0.57 

0.77 

0.96 

1.15 

1.34 

1.53 

1.72 

1/2 

0.850 

2.00 

0.2500 

0  50 

0  75 

1.00 

1.25 

1.50 

1.75 

2.00 

2.25 

9/16 

1.076 

2.25 

0.3164 

0.63 

0.95 

1.27 

1.58 

1.90 

2.21 

2.53 

2.85 

5/8 

1.328 

2.50 

0.3906 

0.78 

1.17 

1.56 

1.95 

2.34 

2.73 

3.12 

3.52 

11/16 

1.608 

2.75 

0.4727 

0.94 

1.42 

1.89 

2.36 

2.84 

3.31 

3.78 

4.25 

3/4 

1.913 

3.00 

0.5625 

1.12 

1.69 

2.25 

2.81 

3.37 

3.94 

4.50 

5.06 

13/16 

2.245 

3.25 

0.6602 

1.32 

1.98 

2.64 

3.30 

3.96 

4.62 

5.28 

5.94 

7/8 

2.603 

3.50 

0.7656 

1.53 

2.30 

3.06 

3.83 

4.59 

5.36 

6.12 

6.89 

15/16 

2.988 

3.75 

0.8789 

1.76 

2.64 

3.52 

4.39 

5.27 

6.15 

7.03 

7.91 

1 

3.400 

4.00 

1.0000 

2.00 

3.00 

4.00 

5.00 

6.00 

7.00 

8.00 

9.00 

1/8 

4.303 

4.50 

1.2656 

2.53 

3.79 

5.06 

6.33 

7.59 

8.86 

10.12 

11.39 

1/4 

5.312 

5.00 

1.5625 

3.12 

4.69 

6.25 

7.81 

9.37 

10.94 

12.50 

14.06 

3/8 

6.428 

5.50 

1.8806 

3.78 

5.67 

7.56 

9.45 

11.34 

13.23 

15.12 

17.02 

1/2 

7.650 

6.00 

2.2500 

4.50 

6.75 

9.00 

11.25 

13.50 

15.75 

18.00 

20.25 

ROUND  BARS. 

1/4 

0.167 

0.785 

0.0491 

0.10 

0.15 

0.20 

0.25 

0.29 

0.34 

0.39 

0.44 

5/16 

0.261 

0.982 

0.0667 

0.15 

0.23 

0.31 

0.38 

0.46 

0.54 

0.61 

0.69 

3/8 

0.375 

1.178 

0.1104 

0.22 

0.33 

0.44 

0.55 

0.66 

0.77 

0.88 

0.99 

7/16 

0.511 

1.374 

0.1503 

0.30 

0.45 

0.60 

0.75 

0.90 

1.05 

1.20 

0.35 

1/2 

0.667 

1.571 

0.1963 

0.39 

0,59 

0.79 

0.98 

1.18 

1.37 

1.57 

1.77 

9/16 

0.845 

1.767 

0.2485 

0.50 

0.75 

0.99 

1.24 

1.49 

1.74 

1.99 

2.24 

5/8 

1.043 

1.964 

0.3068 

0.61 

0.92 

1.23 

1.53 

1.84 

2.15 

2.45 

2.76 

11/16 

1.262 

2.160 

0.3712 

0.74 

1.11 

1.48 

1.86 

2.23 

2.60 

2.97 

3.34 

3/4 

1.502 

2.356 

0.4418 

0.88 

1.33 

1.77 

2.21 

2.65 

3.09 

3.53 

3.98 

13/16 

1.763 

2.553 

0.5185 

1.04 

1.55 

2.07 

2.59 

3.11 

3.63 

4.15 

4.67 

7/8 

2.044 

2.749 

0.6013 

1.20 

1.80 

2.40 

3.01 

3.61 

4.21 

4.81 

5.41 

15/16 

2.347 

2.945 

0.6903 

1.38 

2.07 

2.76 

3.45 

4.14 

4.83 

5.52 

6.21 

1 

2.570 

3.142 

0.7854 

1.57 

2.36 

3.14 

3.93 

4.71 

5.50 

6.28 

7.07 

1/8 

3.379 

3  .  534 

0.9940 

1.99 

2.98 

3.98 

4.97 

5.97 

6.96 

7.95 

8.95 

1/4 

4.173 

3.927 

1.2272 

2.45 

3.68 

4.91 

6.14 

7.36 

8.59 

9.82 

11.04 

3/8 

5.049 

4.320 

1.4849 

2.97 

4.45 

5.94 

7.42 

8.91 

10.39 

11.88 

13.36 

1/2 

6.008 

4.712 

1.7671 

3.53 

5.30 

7.07 

8.84 

10.60 

12.37 

14.14 

15.90 

RECTANGULAR  BEAMS  WITH  TENSION  REINFORCEMENTS     167 

107.  Shearing  Stresses. — The  distribution  of  shearing  stresses  in 
the  section  of  a  reinforced  concrete  beam  differs  from  that  in  a  homo- 
geneous beam.  The  concrete  between  the  neutral  axis  and  the  steel 
is  not  supposed  to  carry  tension  and  consequently  the  unit  shear  is 
constant  over  this  area.  Fig.  46  represents  a  portion  of  a  reinforced 
beam,  the  length  s  being  very  short,  so  that  the  shear  V.  may  be  the 
same  upon  its  two  ends.  Let  C\  and  €2  represent  the  compression  in 
the  concrete  on  the  two  sides,  and  TI  and  T2  the  corresponding  ten- 
sions in  the  steel.  The  difference  of  tensions  T\ — T2  must  be  commu- 
nicated to  the  concrete  and  carried  as  horizontal  shear  to  the  com- 
pression side  of  the  beam. 


Tfd, 

rc'~* 

^c— 

. 

Neutral  Axis 

V 

V 

Steel 

.Jl 

mm 

Tt 

FIG.  46. 

The  intensity  of  the  horizontal  shear  at  any  point  is  equal  to  the 
intensity  of  the  vertical  shear  at  the  same  point,  as  in  any  beam.  If 
v  is  the  shearing  stress  upon  unit  area  and  6  the  width  of  the  beam,  the 
total  shear  upon  any  horizontal  section  below  the  neutral  axis  is 

vbs=Ti—  T2. 

For  equilibrium  of  the  forces  acting  upon  the  portion  of  the  beam  of 
length  S,  as  shown  in  Fig.  4,  T\ — T2  =  Ci — C2,  and  the  two  couples 
are  also  equal,  or  Vs  =  (Ti — T2)  jd.  Equating  these  values  of  T\ — T2, 
and  reducing,  we  find, 

'     .      -  ,-^.  .   .   .,.   ....   .  .   (io) 

In  designing  reinforced  concrete  beams,  it  is  usual  to  adopt  a 
limiting  value  for  v  and  make  the  section  of  the  beam  large  enough  so 
that  the  safe  value  of  v  as  given  by  the  above  formula  shall  not  be 
exceeded.  The  Joint  Committee  on  Concrete  recommends  that  the 
maximum  value  of  v  shall  not  exceed  6  per  cent  of  the  ultimate  com- 


168 


REINFORCED  CONCRETE 


pressive  strength.  This  gives  v=120  lb./in.2  as  a  safe  value  for 
ordinary  concrete  as  commonly  used  in  structural  work  (with  crush- 
ing strength  of  about  2000  lb./in.2  at  thirty  days). 

Rectangular  beams,  reinforced  for  tension  only,  are  usually  suffi- 
ciently strong  to  resist  direct  shearing  stresses  when  properly  designed 
for  flexural  stresses.  The  areas  of  such  beams  are  not  affected  by 
providing  for  shear,  although  they  may  sometimes  need  reinforcement 
against  diagonal  tension. 

108.  Diagonal  Tension. — The  intensity  of  the  horizontal  shear  at 
any  point  in  a  beam  is  equal  to  the  intensity  of  the  vertical  shear  at 
the  same  point.  In  Fig.  47  let  A  BCD  be  an  extremely  small  prism 


\ 

vsb 

T) 

Sj 

vsb 

/ 

J 

/T* 

vsb 
c* 

s 

s 

vsb 


FIG.  47. — Diagonal  Tension  due  to  Sheat. 


in  a  reinforced  beam,  the  vetical  and  horizontal  dimensions  of  which, 
parallel  to  the  side  of  the  beam,  are  represented  by  s,  and  the  thick- 
ness normal  to  the  side  by  b.  If  v  represent  the  unit  shearing  stress, 
the  shear  acting  upon  each  of  the  four  sides  of  the  prism  is  vsb.  If 
the  two  forces  meeting  at  B  and  the  two  meeting  at  D  be  combined 
into  resultants,  T&,  there  will  result  two  equal  and  opposite  forces 
producing  tension  in  a  diagonal  direction  upon  the  prism.  The  value 


of    this    tension    is    Td  =  — 7=,  and  it  is  distributed  over   an  area, 

V2 

fcs/cos  45°.     The  unit  tension  due  to  shear  is 
Td_  =  2vbs        1 


bsV2     V2 


The  unit  diagonal  tension  due  to  shear  is  therefore  equal  to  the 
unit  shear  and  acts  at  an  angle  of  45°  with  the  axis  of  the  beam. 

As  is  readily  seen  from  Fig.  47,  diagonal  compression  equal  to  the 
diagonal  tension  exists  in  a  direction  at  right  angles  to  the  tension. 
The  diagonal  compression  is  unimportant  and  need  not  be  considered 
in  beam  design,  as  these  stresses  are  always  small  in  comparison  with 


RECTANGULAR  BEAMS  WITH  TENSION  REINFORCEMENTS      169 

the  compressive  resistance  of  the  concrete.  It  is,  however,  commonly 
necessary  to  reinforce  concrete  beams  to  prevent  diagonal  tension 
cracks,  as  failures  of  beams  frequently  occur  from  this  cause. 

In  a  homogeneous  beam,  the  maximum  tension  at  any  point  on 
the  tension  side  of  the  neutral  axis  is  the  resultant  obtained  by  com- 
bining the  diagonal  tension  due  to  shear  with  the  horizontal  tension 
due  to  moment  at  the  same  point.  In  a  reinforced  concrete  beam,  the 
steel  is  supposed  to  carry  all  of  the  horizontal  tension,  and  the  con- 
crete none.  Some  horizontal  tension  will  necessarily  be  carried  by 
the  concrete,  but,  if  sufficient  horizontal  reinforcement  be  used,  the 
reinforcement  for  diagonal  tension  need  provide  only  for  tensions  due 
to  shear. 


FIG.  48. — Diagonal  Tension  Failure. 

Fig.  48  shows  the  form  of  failure  likely  to  occur  from  diagonal 
tension,  where  horizontal  reinforcement  only  is  used.  The  diagonal 
tension  at  c  becomes  greater  than  the  tensile  strength  of  the  con- 
crete and  the  concrete  cracks.  A  horizontal  crack  above  the  steel 
then  follows,  which  separates  the  concrete  from  the  steel  and  causes 
failure. 

The  safe  resistance  of  concrete,  without  reinforcement,  to  diagonal 
tension  is  stated  by  the  Joint  Committee  to  be  about  one-third 
of  the  safe  resistance  to  direct  shear,  or  about  2  per  cent  of  the 
ultimate  compressive  strength.  For  ordinary  concrete,  breaking  at 
2000  lb./in.2  when  twenty-eight  days  old,  reinforcement  against 
diagonal  tension  is  necessary  when  v  is  greater  than  40  lb./in.2. 

Two  methods  of  placing  steel  for  diagonal  tension  reinforcement 
are  commonly  employed. 

(a)  Vertical  stirrups  may  be  used,  designed  to  carry  the  vertical 


170 


REINFORCED  CONCRETE 


component  of  the  diagonal  tension,  leaving  the  horizontal  component 
to  be  taken  by  the  horizontal  tension  steel. 

(6)  The  steel  may  be  placed  at  an  angle  of  45°  with  the  hori- 
zontal and  parallel  with  the  tensions  due  to  shear.  In  this  case  the 
diagonal  steel  must  be  rigidly  connected  with  the  horizontal  steel  to 
prevent  slipping  horizontally,  which  is  often  accomplished  by  bend- 
ing up  part  of  the  horizontal  reinforcement  near  the  end  of  the  beam, 
where  stresses  due  to  moment  are  light. 


__Jee_ 


FIG.  49. — Vertical  Stirrup  Reinforcement. 

Vertical  Stirrups. — Fig.  49  shows  a  beam  reinforced  for  diagonal 
tension  by  the  use  of  vertical  stirrups. 

Let      s  =  length  of  beam  to  be  reinforced  by  one  stirrup; 
V  =  Total  vertical  shear  in  section  s; 
v  =  unit  shearing  stress; 
Td  =  Total  diagonal  tension  in  distance  s; 
Tv  =  Total  vertical  tension  in  stirrup. 


The  average  unit  shear  v  =  r^.     This  is  also  the  unit  diagonal 
tension  due  to  shear,  acting  at  an  angle  of  45°  with  the  horizontal, 


and  the  total  tension  is 
ft 


cos  45 


0     Vs  cos  45° 


en) 


The  vertical  component  of  this  carried  by  the  stirrup  is 

vbs     Vs 


9  .r0 
Tv = vbs  cos2  45    =  -~-  = 


(12) 


RECTANGULAR  BEAMS  WITH  TENSION  REINFORCEMENTS      171 

The  total  area  of  stirrup  required  to  carry  this  stress  is 

_vbs_  Vs  _2AJs_2A,fsjd 

Av~2fs-2f3d  ~vT'     ~T"'     V   '     ' 

The  Joint  Committee  recommends  the  use  of  the  value 

9     VQ  9 

T,  =  ±~     or     Tv=i.vbs, 
3  jd  3 

in  place  of  that  given  in  Formula  (12). 

In  designing  stirrup  reinforcement,  the  spaces  s  may  be  assumed 
and  the  required  area  Av  of  stirrups  computed,  or  the  spacing  may 
be  determined  for  stirrups  of  given  area.  The  value  of  v  to  be  used 
should  be  the  average  value  for  the  space  s. 

In  order  to  avoid  danger  of  cracks  between  stirrups,  the  spaces 
s  should  not  exceed  one-half  the  effective  depth  of  beam,  %d.  The 
shear  is  a  maximum  at  the  support,  and  the  first  space  should  be 
measured  from  the  middle  of  the  bearing  on  the  support. 

Diagonal  tension  reinforcement  is  needed  only  in  the  portion  of 
the  beam  in  which  the  shear  exceeds  the  allowable  unit  shear  for  plain 
concrete  (where  v  is  greater  than  2  per  cent  of  the  ultimate  compress- 
ive  strength  of  the  concrete).  In  a  uniformly  loaded  beam,  the 
shear  is  zero  at  the  middle  of  the  beam  and  increases  uniformly  with 
the  distance  from  the  middle  to  a  maximum  at  the  support.  If 
vm  is  the  maximum  unit  shear  at  the  support  and  I  the  length  of  the 
beam  the  unit  shear  (or  unit  diagonal  tension)  at  any  point  distant 
x  from  the  middle  of  the  beam  is 


Reinforcement  for  diagonal  shear  is  needed  from  the  point  where  v 
equals  the  allowable  shear  for  unreinforced  concrete  to  the  end  of  the 
beam.  For  ordinary  concrete,  in  which  the  allowable  unit  shear  is 
40  lb./in.2,  we  have 

_40[ 

~2vm 

Diagonal  Reinforcement.  —  Fig.  50  represents  a  beam  reinforced 
for  diagonal  tension  by  bars  inclined  at  45°  with  the  horizontal. 
As  before,  if  the  unit  shear  is  more  than  2  per  cent  of  the  ultimate  com- 
pressive  strength  of  the  concrete,  the  beam  needs  reinforcement 
against  diagonal  tension. 

Let  s  be  the  length  of  beam  for  which  the  steel  at  a  is  to  carry 
the  diagonal  tension,  and  Td  the  total  tension  in  the  steel  at  a. 


172 


REINFORCED  CONCRETE 


v  =  j-rjis  the  unit  diagonal  tension  on  the  concrete,  and  bs  cos  45° 

is  the  section  normal  to  the  tension  over  which  this  unit  diagonal 
tension  is  distributed.  The  total  tension  to  be  carried  by  the  steel 
at  a  is 

m       ,  ,e0     Vs  cos  45°       Vs 

Td=vbs  cos  45  = ^ = =..     .  (14) 


\ 


•  u  •  u  • 


FIG.  50. — Diagonal  Reinforcement. 
The  area  of  steel  required  is 

vbs  cos  45°        Vs 


Ad=- 


and 


vb 


(15) 


The  limits  within  which  reinforcement  is  necessary,  and  its  proper 
spacing,  may  be  determined  in  the  same  manner  as  for  vertical  stir- 
rups. Where  diagonal  reinforcement  is  used,  the  spacing  should  not 
exceed  three-fourths  of  the  effective  depth  of  beam  or  s  =  f d. 

Bending  up  Horizontal  Steel. — Diagonal  reinforcement  is  com- 
monly provided  by  bending  up  a  portion  of  the  horizontal  steel  near 
the  supports  where  it  is  not  needed  for  horizontal  tension.  In  a 
simple  beam  uniformly  loaded,  the  moment  diagram  is  a  parabola 
(see  Fig.  51)  and  the  diminution  of  the  moment  from  the  middle 
toward  the  ends  is  proportional  to  the  square  of  the  distance  from  the 
middle  of  the  beam.  Thus  if  M  is  the  moment  at  the  middle 
MX,  the  moment  at  a  point  distant  x  from  the  middle,  and  1/2,  the 
distance  from  the  middle  of  the  beam  to  the  support. 


M-Ma 
M 


. 

(Z/2)2' 


RECTANGULAR  BEAMS  WITH  TENSION  REINFORCEMENTS     173 


or 


M-MX- 


MX* 

(Z/2)2 


(16) 


The  area  of  horizontal  steel  needed  at  any  point  varies  directly 
with  the  moment  at  the  point.  If  A  is  the  area  required  at  the  middle 
and  Ax  the  area  needed  at  any  point  distant  x  from  the  middle, 


A-AX= 


Ax2 


and 


FIG.  51. — Distribution  of  Moment. 

A — Ax  is  the  area  of  steel  that  it  is  allowable  to  turn  up  at  distance 
x  from  the  middle  of  the  beam. 

The  Joint  Committee  does  not  consider  diagonal  tension  reinforce- 
ment to  be  fully  effective  unless  it  is  firmly  attached  to  the  longi- 
tudinal tension  bars.  When  stirrups  are  looped  about  the  longi- 
tudinal steel,  the  Committee  recommends  that  the  allowable  unit 

shear  (#— rm  be  made  4J  per  cent  of  the  ultimate   compressive 

strength,  while  when  fully  reinforced  with  bars  firmly  attached 
6  per  cent  may  be  allowed. 

109.  Bond  Resistance  and  Lateral  Spacing. — The  stress  carried 
by  the  steel  in  a  reinforced  concrete  beam  is  transmitted  to  the  steel 
through  the  bond  existing  between  the  concrete  and  steel. 

Horizontal  Tension  Bars. — The  amount  of  stress  that  may  be 
transmitted  to  the  horizontal  steel  at  any  cross-section  of  the  beam 
is  equal  to  the  horizontal  shear  at  the  section. 


174  REINFORCED  CONCRETE 

y 

Let  v  =  r-r-,  =  the  unit  horizontal  shear  in  the  concrete  at  any 
bjd 

section; 

w  =  the  unit  bond  stress  between  the  steel  and  concrete; 
So = total  circumference  of  steel  bars  in  the  section; 
6  =  width  of  beam. 

Y 

The  total  horizontal  shear  for  unit  length  of  beam,  bv  =  ^ 

then 

u  =  ~  =  -^TJ,       (19) 

and 

So  =  — =-  (20) 

u     ujd 

If  u  does  not  exceed  the  safe  unit  bond  stress  between  the  steel 
and  concrete  at  the  section  of  maximum  shear,  the  horizontal  shear 
may  be  communicated  to  the  steel  without  danger  of  the  bars  slipping. 
The  Joint  Committee  recommend  that  the  safe  bond  stress  between 
concrete  and  plain  reinforcing  bars  be  limited  to  4  per  cent  of  the 
compressive  strength  of  the  concrete,  and  for  good  deformed  bars 
not  to  exceed  5  per  cent.  For  ordinary  concrete  (compression 
2000  lb./in.2)  this  would  give  a  value  for  plain  bars,  u  =  80  lb./in.2,  and 
for  the  best  deformed  bars,  w=100  lb./in.2 

In  selecting  sizes  of  bars  for  horizontal  tension  steel,  care  should 
be  taken  that  the  bars  are  not  too  large  to  give  sufficient  surface 
area  to  provide  properly  for  bond  stress.  Thus,  suppose  a  beam, 
in  which  6  =  6  inches,  d=10  inches,  and  .7  =  0.85,  requires  for  tension 
steel,  A  =0.60  in.2  If  the  maximum  value  of  shear  7  =  3200  Ib. 
and  allowable  unit  bond  stress  u  =  80  lb./in.2,  the  required  surface 
area  of  steel  per  inch  of  length, 

-        V  32°°       =4.7  in.* 


Referring  to  Table  X,  we  find : 

For   two     f-in.  round  bars,  A  =0.61  and  So  =  2X1.96  =  3.92  in.2 

three  J-in.  round  bars,  A  =  0.59  and  So  =  3  X  1.57 =4.71  in.2 

four  ^-in.  round  bars,  A  =  0.60  and  So  =  4 XI. 37  =  5.48  in.2 

six     i^-in.  square  bars,  A  =  0.59  and  So  =  6  X  1.25  =  7.50  in.2 

The  f-inch  bars  are  too  large  for  the  bond  stress;  the  J-inch  bars  are 
just  sufficient;  the  j^-inch  bars  are  still  better  and  would  probably 
be  selected. 


RECTANGULAR  BEAMS  WITH  TENSION  REINFORCEMENTS      175 

Length  of  Bar  to  Prevent  Slipping.  —  The  stress  carried  by  any 
reinforcing  bar  must  be  transmitted  to  the  concrete  between  the 
point  at  which  the  stress  exists  and  the  end  of  the  bar,  which  must  be 
accomplished  either  by  having  a  sufficient  length  of  bar  to  develop 
bond  stress  equal  to  the  maximum  tension  or  by  anchoring  the  bar 
by  other  means. 

Let    fs  =  tensile  stress  per  square  inch  in  the  bar; 
i  =  diameter  of  bar  in  inches; 
u  =  allowable  bond  stress  per  square  inch; 
lb  =  length  required  for  bond. 

•  9  /• 

For  round  bar.  the  total  stress  =  -~~-  =  irilbU. 

4 

For  square  bars,  the  total  stress  =  i2fs=4ilbu. 
Then  for  either  round  or  square  bars, 


<»> 


If  /,=  16,000  lb./in.2  and  it  =  80  lb./in.2,  Z&  =  50z,  or  for  safety, 
the  length  between  the  point  where  the  stress  of  16,000  lb./in.2 
exists  and  the  end  of  the  bar  must  be  50  diameters. 

Anchoring  Bar  by  Bending.  —  When  it  is  not  feasible  to  secure  the 
length  of  bar  necessary  for  bond,  the  end  of  the  bar  may  be  anchored 
in  the  concrete  by  bending  to  a  semi-circle.  Experiments  indicate 
that,  in  general,  the  full  strength  of  a  bar  in  tension  may  be  developed 
by  bending  the  end  to  a  semicircle,  the  diameter  of  which  is  four 
times  the  diameter  of  the  bar.  Short  right-angled  bends  are  found 
to  be  much  less  effective  than  curves  through  180°. 

In  the  case  of  restrained  beams,  or  cantilevers,  when  maximum 
tension  occurs  near  the  support,  careful  attention  must  be  given  to 
the  anchorage  of  the  bars.  Bars  used  for  diagonal  tension  reinforce- 
ment, either  vertical  stirrups  or  inclined  bars,  have  maximum  tension 
at  the  neutral  axis,  and  must  have  a  sufficient  embedment  on  the  com- 
pression side  of  the  neutral  axis  to  resist  the  maximum  tension  in  the 
steel. 

Lateral  Spacing  of  Steel.  —  The  horizontal  tension  rods  in  a  rein- 
forced concrete  beam  must  be  so  spaced  as  to  leave  a  sufficient  area  of 
concrete  between  them  to  carry  the  shear  communicated  to  the  con- 
crete by  the  portion  of  the  bars  below  the  minimum  section  of  con- 
crete. This  would  require  that  for  circular  bars  the  horizontal  sec- 
tion between  rods  be  capable  of  carrying  a  shearing  stress  equal  to  the 


176  REINFORCED  CONCRETE 

bond  stress  on  the  lower  half  of  the  bars.     If  sc  be  the  clear  spacing 
between  the  bars  and  i  the  diameter  of  the  bar,  for  the  round  bar 

iriu  iriu 

s°v  =  ~2      or    S<=W 

For  the  values  of  unit  stress  recommended  by  the  Joint  Com- 
mittee (v  =  6  per  cent  and  u=4  per  cent  of  the  ultimate  compressive 

ftiM 

strength),  v  =  %u,  and  for  round  bars,  sc  =  ^-=l.05i. 

For  square  bars  with  sides  vertical,  scv  =  3iu,  or  sc  =  2i,  and  for 
square  bars  with  diagonals  vertical,  sc  =  •§•*. 

For  deformed  bars  these  values  would  be  increased  in  the  ratio 
of  5  to  4. 

The  Joint  Committee  recommends  1  that: 

The  lateral  spacing  of  parallel  bars  should  not  be  less  than  three  diameters  from 
center  to  center,  nor  should  the  distance  from  the  side  of  the  beam  to  the  center 
of  the  nearest  bar  be  less  than  two  diameters.  The  clear  spacing  between  two 
layers  of  bars  should  be  not  less  than  1  inch.  The  use  of  more  than  two  layers 
is  not  recommended,  unless  the  layers  are  tied  together  by  adequate  metal  con- 
nections, particularly  at  and  near  points  where  bars  are  bent  up  or  bent  down. 
Where  more  than  one  layer  is  used  at  least  all  bars  above  the  lower  layer  should 
be  bent  up  and  anchored  beyond  the  edge  of  the  support. 

110.  Design  of  Beams.  —  The  methods  of  applying  formulas  and 
tables  in  the  design  of  rectangular  beams  is  illustrated  in  the  following 
examples  : 

(7)  Design  a  rectangular  beam  to  have  a  span  of  25  feet  and 
carry  a  uniform  load  of  600  pounds  per  linear  foot,  in  addition  to  its 
own  weight,  using  working  stresses  recommended  by  the  Joint  Com- 
mittee for  concrete  of  2000  lb./in.2  compressive  strength. 

Solution.—  From  Table  VII,  for  ft  =15,  /,  =  16,000  and  fc  =  650, 
we  find  fl  =  108,  p  =  .0078,  j=.874. 

Assume  weight  of  beam  =  300  pounds  per  linear  foot. 


Then  jf--  ^rc  in..lb. 

o  o 


843750/108  =  7812,  and  for  6=12,  d  =  25.5, 
for  6  =  14,  d  =  23.6     Taking  6  =  14  and  total  depth,  ft  =  25.5,  weight 
of  beam  =  14X25.  5X150/144  =  372   pounds   per  linear  foot.     The 
assumed  load  is  too  small.     Assume  weight  of  beam  =400  pounds 
per  linear  foot. 


o  lUo 

1  Proceedings,  American  Society  of  Civil  Engineers,  December,  1916. 


RECTANGULAR  BEAMS  WITH  TENSION  REINFORCEMENTS     177 


For  6=14,  d  =  -J-^j-=24.9.     Using  6  =  14  and  d  =  25,  make  ft  =  27. 


27X14X150 
Then  weight  of  beam  =  —       ^  --  =  394  pounds  per  linear  foot, 

which  agrees  with  the  assumption. 

Horizontal  steel,  A  =pdb  =  .  0078X14X25  =  2.73  in.2 
From  Table  X,  seven  f-inch  square  bars  give  A  =2.73  in.2 
five      f-inch  square  bars  give  A  =2.81  in.2 
six       f-inch  round  bars  give  A  =2.65  in.2 

Seven  f-inch  square  bars,  spaced  1|  inch  c.  to  c.  or  six  f-inch  round 
bars,  spaced  2J  inches  c.  to  c.  might  be  placed  in  the  width  of  14 
inches,  meeting  the  requirement  of  spacing  3  diameters  c.  to  c.  We 
will  use  five  f-inch  square  bars,  spaced  2J  inches  c.  to  c.  and  2  inches 
from  side  of  beam. 

,,     .          0,         T7     co    25X1000     10™1U 
Maximum  Shear,  V  =  ^  =  --  ~  -  =  12,500  Ib. 

Z  2i 

V  12500 


The  section  is  sufficient  for  shear,  and  no  diagonal  tension  reinforce- 
ment is  necessary. 

Bond  Stress,  Table  X,  for  five  f-inch  bars,  2o  =  5X3.00  =  15  in.2 
and  (19) 

bv      14X40.6     Q.ftl,    ,.    o 
U  =  2o  =    IS"   =37'91b-/m.2, 

which  is  less  than  the  allowable  stress. 

8.  A  simple  beam  of  10-foot  span  to  center  of  bearings,  is  to  carry 
a  load  of  400  pounds  per  linear  foot.  Design  the  beam,  assuming 
n  =  15.  fs=  15,000  lb./in.2,  /c  =  750  lb./in2,  safe  value  of  unit 
shear  =120  lb./in.2,  and  for  diagonal  tension  on  concrete  =40  lb./in.2 

Solution.  —  Assuming  the  weight  of  beam  as  65  pounds  per  linear 
foot,  the  total  load  is  (400+65)10  =  4650  pounds. 

,,     1   ,     4650X10X12    ftfV7Kn.     „ 
M  =  %ul  =  --  ^—     —  =  69750  in.-lb. 

o 

From  Table  VII,  f  or  fs=  15,000,  /c=750,  and  n=15,  we  have 
R  =  138,  j  =  0.857,  and  p  =  .0107. 

then   &d2=M/#  =  69750/138  =  505.    If  we  assume   6  =  5,   we  find 
d  =  10,  and  A  =  pbd  =  .0107  X  5  X  10  =  0.535  in.2 
By  Table  X,  five      f-inch  round  bars  =  .55  in.2 
four     f-inch  square  bars  =  .56  in.2 
three  j^-inch  square  bars  =  .57  in.2 


178  REINFORCED  CONCRETE 

The  four  f  -inch  square  bars  will  fit  in  the  width  of  beam  with  proper 
spacing,  but  we  will  use  three  y^-inch  bars. 

If  the  concrete  extend  1J  inches  below  the  center  of  the  steel, 
/i=d-j-li  =  lli  inches,  and  the  weight  of  beam  is  5X11.5X150/144 
=  60  lb./ft.;  this  is  a  little  less  than  our  assumed  weight. 

Maximum  Shear, 

V 


This  is  less  than  120  lb./in.2,  and  the  dimensions  of  the  beam  are 
sufficient. 

Reinforcement  for  diagonal  tension  is  needed  beyond  the  point 

401    40X10 

where  v  =40  lb./m.2,  or  x  =  ^—  =          .  =  3.7  feet.    Reinforcement  is 

2vm      2  X  o4 

required  to  5—3.7  =  1.3  foot  =  15.6  inches  from  the  support. 

Vertical  Stirrups.  —  If  we  assume  s  =  %d  =  5  inches  for  the  stirrup 
next  the  support,  we  have  (13). 

vbs     54X5X5 


For  U-shaped  stirrup,  the  section  of  rod  required  will  be  one-half 
of  this,  or  0.045  in.2  one-quarter  in  round  bars  are  sufficient,  and 
three  stirrups  may  be  used,  spaced  3,  8,  and  13  inches  from  the 
middle  of  support. 

Bond  Stress.— For  the  horizontal  steel,  Table  X,  2o  =  3X1.75 
=  5.25  in.2,  and  (19)  u  =  bv/2o  =  5X54/5.25  =  51.4  lb./in.2,  which  is 
less  than  the  allowable  bond  stress,  and  no  anchoring  is  necessary. 

fi        15000 
For  the  vertical  stirrups   (21)   ^=1^=.  =11.8  inches, 

or  the  stirrups  need  11.8  inches  above  the  neutral  axis  for  anchor- 
age; they  must  therefore  have  hooked  ends. 

ART.  29.    T-BEAMS  WITH  TENSION  REINFORCEMENT 

111.  Flexure  Formulas. — In  a  rectangular  reinforced  concrete 
beam,  in  which  the  steel  carries  all  the  tension,  the  area  of  concrete 
below  the  neutral  axis  does  not  affect  the  resisting  moment  of  the 
beam.  The  office  of  this  concrete  is  to  hold  the  steel  in  place  and 
carry  the  shear,  thus  connecting  the  steel  with  the  compression  area 
of  concrete. 

In  a  T-beam,  the  flange  carrying  the  compression  is  connected 
with  a  narrow  web  which  holds  the  steel,  as  shown  in  Fig.  52.  When 
the  neutral  axis  is  in  the  flange,  such  a  beam  may  be  computed  by  the 


T-BEAMS   WITH  TENSION  REINFORCEMENTS 


179 


formulas  and  tables  used  for  a  rectangular  beam,  using  the  width  of 
the  flange,  b,  as  the  width  of  the  beam. 


-1 

Jcd\      ~ 
i  

—  i 

JfZaZZ        ~- 

ci 


b' 


FIG.  52. — T-Beam  with  Tension  Reinforcement. 

When  the  neutral  axis  is  below  the  bottom  of  the  flange  of  the 
T-beam,  the  compression  area  is  less  than  that  of  the  rectangular 
beam,  and  special  formulas  are  necessary.  Fig.  52  represents  a 
beam  of  this  kind.  The  amount  of  compression  on  the  web  is  usually 
very  small  and  may  be  neglected  without  material  error,  thus  greatly 
simplifying  the  formulas. 

The  same  notation  will  be  employed  as  in  the  rectangular  beam, 
letting  b  =  width  of  flange; 
6'  =  width  of  web; 
t  =  thickness  of  flange. 

The  position  of  the  neutral  axis  in  terms  of  the  unit  stresses  may 
be  found  as  in  the  rectangular  beam,  giving 


and 


fc 


(22) 
(23) 


The  average  unit  compression  on  the  flange  is  the  half  sum  of 
the  compressions  at  the  top  and  bottom  of  the  flange,  or 


The  total  compression  on  the  concrete  is 

2kd-t 
C  =/c    „-,  •,    bt. 


2kd 


This  is  the  equal  to  the  total  tension  on  the  steel, 

T=fsA=fspbd. 


(24) 
(25) 


180  REINFORCED  CONCRETE 

From  the  equality  of  (24)  and  (25)  we  find 

(2k-t/d)  t 

P=2n(li=W'd>       ••••   -    •    V    *     (26) 
and 

fc.^+M/f.      .....       .    (27) 

pn+t/d 

The  distance  of  the  centroid  of  compression  from  tne  upper  face 
of  the  beam  is 

3k-2t/d  i_ 
2k-t/d  '3' 
therefore 


(28) 


2kt/d   3 
The  resisting  moment  of  the  beam  is 

.-V       .     .     .     (29) 


or 

Examples. — The  use  of  these  formulas  in  the  solution  of  problems 
arising  in  the  design  or  investigation  of  T-beams  are  illustrated 
in  the  following  examples : 

9.  A  T-beam  has  the  following  dimensions,  6  =  48  inches,  £  =  4 
inches,  d  =  22  inches,  6' =  10  inches.  The  steel  reinforcement  con- 
sists of  six  j-inch  round  rods.  If  the  safe  unit  stresses  of  steel  and 
concrete  are  15,000  and  600  lb./in.2  respectively,  and'n  =  15,  what 
is  the  safe  resisting  moment  of  the  beam? 

Solution.— From  Table  X,  A  =2.65  in2,  and  p  =  00^Q  =  .0025; 
formula  (27)  gives 


.0025X15+ A 

Using  (28)  we  find 

M-22    3X.247-2(^)  4 
Jd~22      2X.247-A      3-20"39' 

From  (22), 

/,_  15(1-.  247) 

T~  ~^T 

If  /c  =  600  lb./in.2,  /,  =  600X45.7  =  27,420  lb./in.2 
This  is  greater  than  the  safe  unit  stress  on  steel,  and  the  safe  moment 
will  be  that  which  causes  a  stress  of  15,000  lbs./in.2  on  the  steel,  or 
from  (29), 

M  =  2.65  X 15000  X  20.39  =  810000  in.-lb. 


T-BEAMS   WITH  TENSION  REINFORCEMENTS  181 

10.  The  flange  of  the  T-beam  is  26  inches  wide  and  4  inches 
thick.  The  beam  is  to  carry  a  bending  moment  of  520,000  in.-lb. 
The  safe  unit  stresses  for  concrete  and  steel  are  600  and  16,000 
lb./in.2  respectively.  What  area  of  steel  and  depth  of  beam  are 
needed. 

Solution.-*?    (23)    fc=160010^165°;600  =  .360.     We   must   now 

find  d  by  assuming  values  and  testing  their  suitability.     Try  d—  18; 
from  (28)  we  have 

4 
" 


'  2X.360-A     3 

(9)  gives  C  =  M/jd  =  520000/16.3  =  31900. 


From  (24)  /c  =  07       .-fa  =  440  lb./in.2    This  is  a  safe  value,   but 

t 


~2kd~ 

a  less  depth  will  answer.  Trying  15  inches,  we  find  C  =  38,000 
pounds,  and  /c  =  580  lb./in.2;  15  inches  is,  therefore,  approximately 
the  minimum  value  for  d.  For  this  value  of  d}  Formula  (25)  gives, 

A  =  T/fs  =  38000/15000  =  2.375  in.2 

Width  of  Flange.  —  T-beams  without  lateral  reinforcement  in  the 
flanges  should  have  a  width  of  flange  not  more  than  three  times  the 
width  of  web,  6  =  36'.  When  the  flange  is  reinforced  at  right  angles 
to  the  length  of  beam,  as  in  a  slab  floor  with  T-beams  support,  experi- 
ence indicates  that  the  flange  may  overhang  the  web  on  each  side 
to  a  distance  equal  to  five  or  six  times  the  thickness  of  flange,  and  still 
act  satisfactorily  as  compression  area  for  the  beam.  If  the  width  of 
flange  be  greater  than  this,  the  extra  width  is  of  little  value  and 
should  not  be  considered  in  estimating  the  strength  of  the  beam. 

The  Joint  Committee  has  recommended  the  following  rules  for 
determining  flange  width: 

In  beam  and  slab  construction  an  effective  bond  should  be  provided  at  the 
junction  of  the  beam  and  slab.  When  the  principal  slab  reinforcement  is  parallel 
to  the  beam,  transverse  reinforcement  should  be  used  extending  over  the  beam 
and  well  into  the  slab. 

The  slab  may  be  considered  an  integral  part  of  the  beam,  when  adequate 
bond  and  shearing  resistance  between  slab  and  web  of  beam  is  provided,  but  its 
effective  width  shall  be  determined  by  the  following  rules: 

(a)  It  shall  not  exceed  one-fourth  of  the  span  length  of  the  beam. 

(6)  Its  overhanging  width  on  either  side  of  the  web  shall  not  exceed  six  times 
the  thickness  of  the  slab. 

In  the  design  of  continuous  T-Beams,  due  consideration  should  be  given  the 
compressive  stress  at  the  support. 


182  REINFORCED  CONCRETE 

Beams  in  which  the  T-form  is  used  only  for  the  purpose  of  providing  additional 
compression  area  of  concrete  should  preferably  have  a  width  of  flange  not  more 
than  three  times  the  width  of  the  stem  and  a  thickness  of  flange  not  less  than 
one-third  of  the  depth  of  the  beam.  Both  in  this  form  and  in  the  beam  and  slab 
form  the  web  stresses  and  the  limitations  in  placing  and  spacing  the  longitudinal 
reinforcement  will  probably  be  controlling  factors  in  design. 

112.  Shear  and  Bond  Stresses.  —  Stresses  due  to  shear  in  the 
concrete  and  bond  stresses  between  the  steel  and  concrete  in  T-beams 
are  found  by  the  same  methods  that  are  used  for  rectangular  beams. 
The  shearing  and  diagonal  tension  stresses  must  be  carried  by  the 
web  of  the  beam,  the  area  of  flange  not  being  considered  in  finding 
unit  shear.  Using  the  same  notation  as  for  rectangular  beams  and 
letting  b'  represent  the  width  of  the  web  of  the  T-beam,  the  formulas 
as  applied  to  T-beams  become: 

y 
For  shear,  v  =  r^, 

and 

b'd  =  -..  (33) 

vj 

For  vertical  stirrups, 

__vb's      Vs 

Av~2fs 

or 


For  diagonal  steel, 

vVs      Vs 


~w, 

or 

s  =  2~^ (35) 

For  point  where  it  is  allowable  to  turn  up  steel, 

A~Ax=W2?' 
and 

X  =  L^A*.  ,  fc.  .,    -<1: ,.';"  .    .    .     (36) 

For  bond  stress, 

b'v       V 


and 

20  =  —  =-^ (37) 


T-BEAMS  WITH  TENSION  REINFORCEMENTS  183 

For  length  of  bar  to  prevent  slipping, 

'•  "'•'•;'••        fc-.      .-!  .    ,    ,    .'V   >..,    ,     (38) 


The  Width  of  the  Web  (&')  must  be  sufficient  to  provide  proper 
area  for  carrying  shear,  as  shown  in  (33),  and  also  to  allow  for  properly 
spacing  the  steel,  as  explained  in  Section  109.  b'  should  not  usually 
be  taken  at  less  than  d/3,  except  in  heavy  beams  where  a  thickness  of 
d/4.  may  be  allowable.  The  value  of  j,  when  not  known,  may  be 
assumed  as  {  without  material  error,  and  the  value  of  vj  in  (33)  may 
be  taken  as  f  of  the  allowable  unit  shear. 

113.  T-Beam  Diagrams.  —  The  labor  of  T-beam  computations 
may  be  considerably  lessened  by  tabulation  'of  some  of  the  terms 
which  enter  into  the  formulas.  Some  of  these  tabulations  are  here 
given  in  the  form  of  diagrams. 

If  we  place  Q=fcj  --  ^,      ,  Q  will  be  constant  for  any  particular 

values  of  unit  stresses  and  t/d.     Substituting  in  Formula  (30)  we 
obtain  M  =  Qbtd  and  M/bt  =  Qd  or 

Q  =  M/W.     ....    ,     .     .     .     (39) 

In  Diagram  I,  values  of  fc  and  p  are  given  in  terms  of  various 
values  of  d/t  and  Q  for  n  =  15  and  fs  =  16,000.  This  diagram  may  be 
used  in  design  of  beams  when  these  units  are  to  be  employed,  or 
similar  diagrams  may  easily  be  prepared  for  other  values  of  fs  and  n. 

Diagram  II  gives  values  of  p  and  j  in  terms  of  fs/fc  and  d/t,  when 
n  =  15.  This  diagram  may  be  used  in  reviewing  a  beam  of  known 
dimensions  and  reinforcement,  or  in  design  when  values  of  fs  other 
than  that  used  in  Diagram  I  are  to  be  employed. 

Examples.  —  The  following  examples  illustrate  the  use  of  these 
diagrams  and  formulas  in  computation. 

11.  A  T-beam  has  dimensions  as  follows:  b  =  45  inches,  t  —  4  inches, 
d  =  20  inches,  bf  =  9  inches.  It  is  reinforced  with  ten  f-inch  round 
steel  bars.  If  the  safe  unit  stresses  of  steel  and  concrete  are  16,000 
and  650  lb./in.2  respectively,  what  is  the  safe  resisting  moment  for 
the  beam? 

4  41S 

Solution.—  Table   X,  A  =  .4418X10=4.418   in.2,    and  p=     '     °- 

4o  X  2\j 

=  .0049.     From   Diagram   II,    for   p  =  .0049   and    d/t  =  5,   we   find 
/•//«  =  29,  and  j  =  .914.    If  /c  =  650,  /.  =  650X29  =  18850.    This   is 


184 


REINFORCED  CONCRETE 


more  than  is  allowable,  and  the  safe  resisting  moment  is  that  giving 
a  stress  of  16,000  on  the  steel,  or  using  (29) 


=  1,292,800  in./lb. 

12.  The  dimensions  of  aT-beam  are,  6  =  36  in.,  t  =  3  in.,  d=  13  in., 
The  beam  is  reinforced  with  six  J-inch  round  steel  bars.     If  this 


£=  16,000 

3.0       3.5       4.0       4.5        5.O       5.5        6.O       6.5      7.0 


r  •      _     •  ^  *     *  •-"•'-^  i  i  i  i  i  i  •  i  i  i  i  •  i  i  _i  i  • 

£.5     3.O       5.5       4.O       4-.S       5.O       5.5       6.0       6.5       7.0 

VALUES  OF 


150 


150 


DIAGRAM  I — for  T-Beam  Design. 

M/bt=Qd. 

beam  is  subjected  to  a  bending  moment  of  550,000  in.-lb.,  what  are 
the  stresses  in  the  steel  and  concrete  respectively? 

2  65 

Solution.— A  =  .4418  X  6  =  2.65      in.2,      and      p  =  ^^3  =  •  0057. 

d/t=  13/3 =4.33.     From  Diagram  II,  we  find  fs/fe  =  27.5  and  j=. 903. 

CCrVAAf) 

Formula  (29)  now  gives  /»  =  2.65x  903X13  =  1827°  lb'/in'2' 
which  fe  =  18270/27.5  =  660  lb./in.2 


T-BEAMS  WITH  TENSION  REINFORCEMENTS 


185 


13.  The  flange  of  a  T-beam  is  to  be  30  inches  wide  and  5  inches 
thick.  The  beam  is  to  sustain  a  bending  moment  of  930,000  in.-lb., 
and  a  maximum  shear  of  14,500  pounds.  The  safe  unit  stresses 


4-5 


10 


15 


10 


a.5      3.0     3.5      4:0     4-.S       5.0     5.5       6.0     6.5      70 
VALUES  OF     *% 

DIAGRAM  II — for  Review  of  T-Beam. 

on  steel  and  concrete  are  16,000  and  650  lb./in.2,  and  maximum 
unit  shear  120  lb./in.2  What  dimensions  of  web  and  area  of  steel 
are  required? 

V     14500 
Solution. — Assuming  j  —  f,  ^'=105,  and  from  (33)  b'd  =  —  = 

vj       luo 


186  REINFORCED  CONCRETE 

=  138  in.2  For  6'  =  8,  d=18  or  for  b'  =  7,  d  =  20  inches.  Either 
of  these  values  would  give  proper  form  to  the  web.  The  deeper 
beam  will  require  less  steel  and  may  be  used  provided  it  gives  suf- 
ficient width  for  placing  the  steel,  and  if  the  stress  upon  the  concrete 
is  satisfactory.  Assume  d  =  2Q  inches.  Then  d/t=4  and  (31) 

930000 
^==3QX5X20==31Q'     "^°r  tnese  va^ues   Diagram   I   gives  /c  =  540 

lb./in.2  and  p  =  .0054.    A  =pbd  =  .  0054X20X30  =  3.24  in.2  and  (20) 


From  Table  X,  for 

six  f-inch  square  bars,  A  =3.37  in.2,  2o=  18.0  in. 
four  j^-inch  square  bars,  A  =3.  52  in.2,  2o  =  15.0  in. 
four  1-inch  round  bars,  A  =3.  14  in.2,  2o=12.56  in. 

The  four  ^f-inch  bars  could  be  placed  in  the  7-inch  width  of  web 
in  two  rows  (see  Section  109).  The  six  f-inch  bars  need  a  width 
of  at  least  7\  inches  and  could  be  used  in  two  rows  by  increasing  the 
width  of  web  by  J  inch. 

If  d  be  made  21  inches,  the  steel  needed  would  be  A  =3.  09  in.2 
and  the  four  1-inch  round  bars  could  be  used  in  two  rows  in  the 
7-inch  width.  At  ordinary  prices,  the  saving  in  steel  would  more 
than  pay  for  the  increased  amount  of  concrete,  and  this  would  make 
the  cheapest  beam. 

ART.   30.     BEAMS  REINFORCED   FOR   COMPRESSION 

114.  Flexure  Formulas.  —  It  is  frequently  necessary  to  place  steel 
in  the  compression  as  well  as  the  tension  side  of  a  beam.  When  the 
size  of  a  rectangular  beam  is  limited,  so  that  the  concrete  area  is 
insufficient  to  carry  the  stress,  steel  may  be  used  to  take  the  surplus 
compression.  In  this  case  the  concrete  and  steel  act  together,  and 
the  stress  upon  the  steel  must  be  limited  to  such  an  amount  as  will 
not  overtax  the  compressive  strength  of  the  concrete. 

In  this  discussion,  the  following  notation  will  be  used,  in  addition 
to  that  employed  for  rectangular  beams  : 

A'  =  area  of  cross-section  of  compression  steel; 

p'  =  ratio  of  compression  steel  area  to  effective  area  of  beam, 

(p'=A'/bd); 
d'=  depth  of  center  of  gravity  of  compression  steel  below 

compression  face  of  beam; 
/'s=unit  stress  in  compression  steel; 
C'  =  total  compression  on  steel. 


BEAMS  REINFORCED  FOR  COMPRESSION  187 

The  same  principles  apply  in  this  case  as  in  that  of  the  beam 
reinforced  for  tension  only,  and  the  concrete  is  supposed  to  carry 
compression  but  no  tension.  It  is  easily  seen  that 


f.-f.^J^, 

and  that 

Compression  on  concrete, 

(41) 


and  compression  on  steel, 

C'  =  A'f',=f',p'bd (42) 

Tension  on  steel, 

'  =  Afs=fspbd (43) 


Substituting  (41)  and  (42)  in  (43)  and  combining  with  (39)  and 
(40)  we  find 

-n(p-pf).      .     .     (44) 

Taking  moments  about  the  tension  steel,  we  find  the  resisting 
moment  of  the  beam, 

M  =  Cjd+C'(d-dr) •  (45) 

Example. — The  use  of  these  formulas  in  design  will  be  illustrated 
by  the  following  example : 

14.  A  beam  whose  dimensions  are  6  =  12  in.,  d  =  22  in.,  d'  =  2 
in.,  is  to  carry  a  bending  moment  of  1,100,000  in.-lbs.  The  safe 
unit  stresses  are  700  and  16,000  lb./in.2  for  concrete  and  steel 
respectively,  n  =  15.  Find  the  areas  of  steel  required. 

Solution. — For  the  given  stresses  (Table  VII),  A;  =  .397  and 
.;  =  .868.  Formula  (41)  gives 

700 
C  =  -^  X  .397  X 12  X  22  =  36680  pounds. 

From  (45), 

1, 100,000- 36680  X  .868X22 

20 
By  Formula  (40), 

OQ7 2 

/',  =  15 X 700 X       '     22  =  8085  lb./in 2 


188  REINFORCED  CONCRETE 

and  (42) 

A'  =  19980/8085  =  2.47  in.2 

Area  of  tension  steel  (43), 

T    36680+19980 


115.  Tables.  —  The  labor  of  computation  may  be  materially 
lessened  by  the  use  of  tables,  which  may  be  made  in  several  ways,  of 
which  the  following  seem  most  convenient  for  use. 

Table  XI.     Transposing  the  terms  of  formula  (43)  we  have 

r    c1 

A  -     -4- 
A  —  f  T"5T« 

Js      Js 

This  may  be  placed  in  the  form, 

A=Plbd+^p,     .......     (46) 

Js 

in  which  p\  is  the  ratio  of  steel  for  a  beam  with  the  same  unit  stresses 
and  without  compression  steel. 

Formula  (45)  may  be  put  in  the  form 

M  =  Rbd2+f'sA'(d-d'), 
or  solving  for  A' 


-fs(d-d'y 

Values  of  R,  pi  and  f's,  in  terms  of  various  values  of  fs,  fc,  and  d'/d 
for  n=15,  are  given  in  Table  XI.  This  table  may  be  used  to  find 
the  areas  of  steel  required  when  a  beam  of  given  dimensions  must 
carry  a  bending  moment  too  great  to  be  resisted  by  tension  reinforce- 
ment only. 

Table  XII.     Combining  (41),  (42)  and  (45)  we  have 

M  =  ^fcjkbd2-i-fspf(l  =  d'/d)bd2, 
from  which 

=  ±fcjk+f'sp'(l-d'/d)=G,       ....     (48) 


in  which  G  is  constant  for  definite  values  of  unit  stresses  and  steel 
ratios.  In  Table  XII,  values  of  p'  and  p  are  given  directly  for  various 
values  of  /c  and  G  when  n  =  15  and  /,=  16,000  lbs./in.2 

To  use  this  table  in  design,  it  is  only  necessary  to  find  G  by 
dividing  the  bending  moment  M  by  bd2  for  the  proposed  beam 
and  take  the  required  ratios  of  steel  directly  from  the  table. 


BEAMS  REINFORCED  FOR  COMPRESSION 


189 


TABLE    XI— BEAMS    WITH    COMPRESSION    REINFORCEMENT. 

Values  of  fs  in  terms  of  fs,fc  and  d'/d 

n  =  15 


fs 

fc 

R 

Pi 

VALUES  OF  d'/d. 

.06 

.08 

.10 

.12 

.14 

.16 

.18 

.20 

14,000 

500 

77 

.0062 

6210 

5780 

5350 

4920 

4490 

4060 

3630 

3200 

600 

102 

.0084 

7620 

7160 

6700 

6240 

5780 

5320 

4860 

4400 

700 

128 

.0107 

9030 

8540 

8050 

7560 

7070 

6580 

6090 

5600 

800 

157 

.0133 

10440 

9920 

9400 

8880 

8360 

7840 

7320 

6800 

15,000 

500 

74 

.0055 

6150 

5700 

5250 

4800 

4350 

3900 

3450 

3000 

600 

99 

.0075 

7560 

7080 

6600 

6120 

5640 

5160 

4680 

4200 

700 

125 

.0097 

8970 

8460 

7950 

7440 

6930 

6420 

5910 

5400 

800 

151 

.0118 

10380 

9840 

9300 

8760 

8220 

7680 

7140 

6600 

16,000 

500 

72 

.0050 

6090 

5620 

5150 

4680 

4210 

3740 

3270 

2800 

550 

83 

.0059 

6745 

6310 

5825 

5340 

4855 

4370 

3885 

3400 

600 

95 

.0068 

7500 

7000 

6500 

6000 

5500 

5000 

4500 

4000 

650 

108 

.0078 

8205 

7690 

7175 

6660 

6145 

5630 

5115 

4600 

700 

121 

.0087 

8910 

8380 

7850 

7320 

6790 

6260 

5730 

5200 

750 

134 

.0097 

9615 

9070 

8525 

7980 

7435 

6890 

6345 

5800 

800 

147 

.0107 

10320 

9760 

9200 

8640 

8080 

7520 

6960 

6400 

900 

174 

.0128 

11730 

11140 

10550 

9960 

9370 

8780 

8190 

7600 

18,000 

600 

88 

.0055 

7380 

6840 

6300 

5760 

5220 

4680 

4140 

3600 

700 

113 

.0072 

8790 

8220 

7650 

7080 

6510 

5940 

5370 

4800 

800 

139 

.0089 

10200 

9600 

9000 

8400 

7800 

7200 

6600 

6000 

900 

165 

.0107 

11610 

10980 

10350 

9720 

9090 

8460 

7830 

7200 

20,000 

600 

83 

.0046 

7260 

6680 

6100 

5520 

4940 

4360 

3780 

3200 

700 

106 

.0060 

8670 

8060 

7450 

6840 

6230 

5620 

5010 

4400 

800 

132 

.0075 

10080 

9440 

8800 

8160 

7520 

6880 

6240 

5600 

900 

157 

.0091 

11490 

10820 

10150 

9480 

8810 

8140 

7470 

6800 

A'  = 


M-Rbd* 
f's(d-d')' 


A=Plbd+ 


A'fs 


190 


REINFORCED  CONCRETE 


TABLE  XII.— BEAMS  WITH  COMPRESSION  STEEL 

Values  for  p'. 
/s  =  16,000.     n  =  15.     G  =  M/bd.z 


fc 

G 

P 

VALUES  OF  d'/d 

.06 

.08 

.10 

.12 

.14 

.16 

.18 

.20 

500 

72 

.0050 

.0000 

.0000 

.0000 

.0000 

.0000 

.0000 

.0000 

.0000 

80 

.0056 

.0014 

.0015 

.0017 

.0019 

.0022 

.0025 

.0030 

.0036 

100 

.0070 

.0049 

.0054 

.0060 

.0068 

.0077 

.0089 

.0104 

.0125 

120 

.0085 

.0084 

.0093 

.0103 

.0116 

.0132 

.0153 

.0189 

.0214 

140 

.0100 

.0119 

.0132 

.0146 

.0165 

.0188 

.0216 

.0264 

.0306 

160 

.0115 

.0154 

.0171 

.0190 

.0214 

.0243 

.0280 

.0338 

.0397 

180 

.0130 

.0189 

.0210 

.0233 

.0263 

.0298 

600 

95 

.0068 

.0000 

.0000 

.0000. 

0000 

.0000 

.0000 

.0000 

.0000 

100 

.0072 

.0007 

.0008 

.0009 

.0010 

.0011 

.0012 

.0014 

.0016 

120 

.0086 

.0035 

.0039 

.0043 

.0047 

.0053 

.0060 

.0068 

.0078 

140 

.0100 

.0064 

.0070 

.0077 

.0085 

.0093 

.0107 

.0122 

.0141 

160 

.0114 

.0091 

.0101 

.0111 

.0123 

.0136 

.0155 

.0176 

.0203 

180 

.0127 

.0120 

.0132 

.0145 

.0161 

.0178 

.0202 

.0230 

.0266 

200 

.0140 

.0148 

.0163. 

.0179 

.0199 

.0220 

.0250 

.0284 

.0328 

220 

.0155 

.0176 

.0194 

.0214 

.0237 

.0262 

.0298 

.0338 

.0391 

650 

108 

.0078 

.0000 

.0000 

.0000 

.0000 

.0000 

.0000 

.0000 

.0000 

120 

.0086 

.0015 

.0017 

.0019 

.0021 

.0023 

.0025 

.0028 

.0033 

140 

.0099 

.0041 

.0045 

.0050 

.0055 

.0061 

.0067 

.0076 

.0087 

160 

.0112 

.0067 

.0074 

.0081 

.0089 

.0099 

.0109 

.0124 

.0141 

180 

.0125 

.0093 

.0102 

.0112 

.0123 

.0137 

.0151 

.0172 

.0196 

200 

.0139 

.0119 

.0130 

.0143 

.0157 

.0174 

.0194 

.0219 

.0250 

220 

.0152 

.0145 

.0159 

.0174 

.0191 

.0212 

.0236 

.0267 

.0304 

240 

.0165 

.0171 

.0187 

.0205 

.0225 

.0250 

.0278 

.0315 

.0358 

260 

.0179 

.0197 

.0215 

.0236 

.0259 

.0288 

.0320 

.0363 

.0413 

700 

121 

.0087 

.0000 

.0000 

.0000 

.0000 

.0000 

.0000 

.0000 

.0000 

140 

.0100 

.0023 

.0024 

.0026 

.0029 

.0032 

.0035 

.0040 

.0046 

160 

.0114 

.0046 

.0050 

.0054 

.0060 

.0066 

.0073 

.0082 

.0094 

180 

.0128 

.0070 

.0076 

.0083 

.0091 

.0100 

.0111 

.0125 

.0142 

200 

.0143 

.0094 

.0102 

.0111 

.0122 

.0135 

.0149 

.0167 

.0190 

220 

.0157 

.0118 

.0128 

.0140 

.0153 

.0169 

.0187 

.0210 

.0230 

240 

.0172 

.0142 

.0154 

.0168 

.0184 

.0203 

.0227 

.0252 

.0286 

260 

.0186 

.0165 

.0180 

.0197 

.0215 

.0237 

.0265 

.0295 

.0334 

280 

.0200 

.0189 

.0206 

.0225 

.0246 

.0272 

.0303 

.0337 

.0382 

300 

.0215 

.0213 

.0232 

.0254 

.0277 

.0306 

.0341 

.0380 

.0430 

800 

147 

.0107 

.0000 

.0000 

.0000 

.0000 

.0000 

.0000 

.0000 

.0000 

160 

.0116 

.0013 

.0014 

.0016 

.0017 

.0019 

.0021 

,0023 

.0025 

180 

.0131 

.0034 

.0036 

.0040 

.0043 

.0048 

.0052 

.0058 

.0064 

200 

.0144 

.0055 

.0058 

.0064 

.0069 

.0076 

.0084 

.0093 

.0103 

220 

.0159 

.0075 

.0080 

.0088 

.0095 

.0105 

.0115 

.0128 

.0143 

240 

.0173 

.0096 

.0103 

.0112 

.0122 

.0134 

.0147 

.0163 

.0182 

260 

.0188 

.0116 

.0125 

.0136 

.0148 

.0163 

.0179 

.0198 

.0221 

280 

.0203 

.0137 

.0147 

.0160 

.0174 

.0192 

.0211 

.0233 

.0260 

300 

.0217 

.0158 

.0169 

.0184 

.0200 

.0220 

.0242 

.0268 

.0299 

320 

.0232 

.0178 

.0192 

.0208 

.0227 

.0249 

.0274 

.0303 

.0338 

BEAMS  REINFORCED  FOR  COMPRESSION 


191 


TABLE  XIII.— BEAMS  WITH   COMPRESSION   STEEL 
Values  of  fs/fc  inTerms  of  p  and  p' 


d' 

P' 

VALUES  OF  p 

d 

.008 

.009 

.010 

.011 

.012 

.014 

.016 

.018 

.020 

.022 

.024 

.06 

.004 

28.1 

26.0 

24.3 

22.8 

21.3 

19.3 

17.7 

16.3 

15.1 

14.1 

13.1 

.006 

30.1 

27.8 

26.0 

24.3 

22.9 

20.5 

18.8 

17.3 

16.1 

15.0 

14.0 

.008 

32.1 

29.7 

27.6 

25.9 

24.4 

21.7 

19.8 

18.3 

17.0 

15.8 

14.9 

.010 

34.2 

31.6 

29.4 

27.4 

25.7 

23.2 

21.1 

19.5 

.17.9 

16.7 

15.7 

.012 

36.3 

33.4 

31.0 

29.1 

27.3 

24.5 

22.2 

20.4 

18.9 

17.6 

16.5 

.014 

38.4 

35.3 

32.6 

30.6 

28.7 

25.8 

23.4 

21.6 

19.8 

18.4 

17.3 

.016 

40.5 

37.2 

34.3 

32.2 

30.2 

27.0 

24.6 

22.8 

20.7 

19.3 

18.2 

.018 

42  3 

39.0 

36.1 

33.8 

31.7 

28.3 

25.9 

23.8 

21.7 

20.1 

18.9 

.020 

44.1 

40.8 

37.9 

35.3 

33.2 

29.6 

27.2 

24.8 

22.7 

21.0 

19.7 

.10 

.004 

27.5 

25.6 

23.9 

22.4 

21.1 

19.1 

17.5 

16.1 

15.0 

14.0 

13.1 

.006 

29.2 

27.2 

25.3 

23.7 

22.4 

20.2 

18.5 

17.0 

15.8 

14.8 

13.8 

.008 

30.8 

28.7 

26.7 

24.9 

23.7 

21.3 

19.4 

18.0 

16.7 

15.5 

14.6 

.010 

32.6 

30.1 

28.1 

26.3 

25.0 

22.4 

20.4 

'18.9 

17.6 

16.4 

15.4 

.012 

34.3 

31.5 

•29.5 

27.7 

26.2 

23.5 

21.5 

19.7 

18.4 

17.2 

16.1 

.014 

36.0 

33.1 

30.9 

29.0 

27.4 

24.6 

22.5 

20.6 

19.2 

18.0 

16.9 

.016 

37.6 

34.6 

32.3 

30.2 

28.6 

25.8 

23.5 

21.5 

20.0 

18.7 

17.6 

.018 

38.1 

36.1 

33.7 

31.6 

29.8 

26.9 

24.4 

22.4 

20.8 

19.5 

18.3 

.020 

40.6' 

37.7 

35.1 

32.9 

30.9 

27.9 

25.4 

23.4 

21.6 

20.2 

18.9 

.14 

.004 

26.9 

25.1 

23.4 

22.0 

20.8 

18.8 

17.3 

16.0 

14.8 

13.8 

12.9 

.006 

28.4 

26.4 

24.6 

23.2 

21.9 

19.8 

18.2 

16.8 

15.5 

14.5 

13.6 

.008 

29.8 

27.6 

25.8 

24.3 

23.0 

20.8 

19.0 

17.5 

16.3 

15.2 

14.3 

.010 

31.2 

28.9 

27.0 

25.4 

24.1 

21.8 

19.9 

18.3 

17.1 

16.0 

15.0 

.012 

32.5 

30.2 

28.2 

26.5 

25.1 

22.7 

20.7 

19.1 

17.8 

16.7 

15.7 

.014 

33.7 

31.4 

29.4 

27.6 

26.1 

23.6 

21.6 

19.9 

18.5 

17.4 

16.3 

.016 

34.9 

32.5 

30.5 

28.7 

27.1 

24.5 

22.4 

20.6 

19.2 

18.0 

16.9 

.018 

36.1 

33.7 

31.6 

29.8 

28.1 

25.4 

23.2 

21.3 

19.9 

18.7 

17.5 

.020 

37.1 

34.9 

32.6 

30.8 

29.0 

26.2 

24.0 

22.0 

20.6 

19.3 

18.1 

.18 

.004 

26.1 

24.6 

23.1 

21.7 

20.5 

18.6 

17.1 

15.7 

14.6 

13.6 

12.8 

.006 

26.9 

25.6 

24.1 

22.7 

21.4 

19.4 

17.8 

16.4 

15.3 

14.3 

13.4 

.008 

28.6 

26.6 

25.0 

23.6 

22.3 

20.2 

18.5 

17.1 

15.9 

14.9 

14.0 

.010 

29.6 

27.6 

25.9 

24.5 

23.2 

21.0 

18.3 

17.8 

16.5 

15.5 

14.6 

.012 

30.6 

28.6 

26.8 

25.3 

24.0 

21.8 

20.0 

18.5 

17.2 

16.1 

15.2 

.014 

31.6 

29.6 

27.7 

26.1 

24.8 

22.6 

20.7 

19.2 

17.9 

16.7 

15.8 

.016 

32.6 

30.5 

28.6 

27.0 

25.6 

23.3 

21.4 

19.8 

18.5 

17.3 

16.3 

.018 

33.6 

31.4 

29.4 

27.8 

26.4 

24.1 

22.1 

20.4 

19.1 

17.9 

16.9 

.020 

34.5 

32.2 

30.3 

28.6 

27.2 

24.8 

22.8 

21.0 

19.7 

18.4 

17.4 

192 


REINFORCED  CONCRETE 


TABLE  XIV.— BEAMS  WITH  COMPRESSION   STEEL 

Values  of  N  in  Formula,  Nfc=M/bd; 

n  =  15 


t 

dr 
d 

VALUES  OF  p' 

.002 

.004 

.006 

.008 

.010 

.012 

.014 

.016 

.018 

.020 

16 

.06 

.228 

.252 

.277 

.302 

.327 

.351 

.376 

.401 

.425 

.450 

.10 

.224 

.246 

.267 

.289 

.310 

.331 

.353 

.374 

.395 

.417 

.14 

.221 

.240 

.258 

.276 

295 

.313 

.331 

.349 

.368 

.386 

.18 

.219 

.234 

.250 

.265 

.281 

.297 

.312 

.328 

.343 

.359 

18 

.06 

.217 

.241 

.266 

.290 

.315 

.339 

.364 

.388 

.413 

.437 

.10 

.213 

.234 

.255 

.276 

.297 

.318 

.339 

.360 

.381 

.402 

.14 

.210 

.228 

.246 

.264 

.281 

.299 

.317 

.335 

.353 

.370 

.18 

.207 

.222 

.237 

.252 

.266 

.281 

.296 

.311 

.326 

.340 

20 

.05 

.208 

.232 

.256 

.281 

.305 

.329 

.354 

.378 

.402 

.426 

.10 

.205 

.225 

.246 

.267 

.287 

.308 

.329 

.349 

.370 

.391 

.14 

.201 

.219 

.236 

.253 

.271 

.288 

.306 

.323 

.340 

.357 

.18 

.198 

.212 

.227 

.241 

.254 

.269 

.283 

.297 

.311 

.326 

22 

.06 

.199 

.223 

'.247 

.271 

.295 

.319 

.343 

.367 

.391 

.415 

.10 

.195 

.216 

.236 

.256 

.277 

.297 

.317 

.337 

.358 

.378. 

.14 

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.209 

.226 

.243 

.260 

.276 

.293 

.310 

.327 

.344 

.18 

.187 

.202 

.216 

.229 

.243 

.257 

.270 

.284 

.297 

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24 

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.286 

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.334 

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.267 

.287 

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.249 

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.315 

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.18 

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.207 

.220 

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.246 

.259 

.272 

.285 

.295 

26 

.06 

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.230 

.254 

.277 

.301 

.324 

.348 

.375 

.395 

.10 

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.199 

.218 

.238 

.257 

.277 

.296 

.316 

.335 

.355 

.14 

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.192 

.207 

.223 

.239 

.255 

.271 

.287 

.303 

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.18 

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.185 

.197 

.209 

.222 

.234 

.246 

.259 

.271 

.284 

28 

.06 

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.224 

.247 

.271 

.294 

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.364 

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.10 

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.212 

.231 

.250 

.270 

.284 

.308 

.327 

.346 

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.201 

.216 

.231 

.247 

.263 

.278 

.293 

.309 

.18 

.166 

.178 

.190 

.202 

.214 

.226 

.237 

.249 

.261 

.273 

30 

.06 

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.218 

.241 

.264 

.287 

.310 

.334 

.357 

.380 

.10 

.168 

.187 

.205 

.224 

.243 

.262 

.281 

.300 

.319 

.338 

.14 

.164 

.179 

.194 

.209 

.224 

.238 

.254 

.269 

.284 

.299 

.18 

.160 

.171 

.183 

.194 

.205 

.217 

.228 

.239 

.251 

.262 

32 

.06 

.166 

.188 

.211 

.233 

.256 

.278 

.301 

.323 

.346 

.368 

.10 

.161 

.180 

.199 

.217 

.236 

.254 

.273 

.292 

.310 

.329 

.14 

.157 

.172 

.186 

.201 

.215 

.230 

.244 

.259 

.273 

.289 

.18 

.154 

.165 

.175 

.186 

.197 

.208 

.219 

.229 

.240 

.251 

BEAMS  REINFORCED  FOR  COMPRESSION  193 

Tables  XIII  and  XIV.  If  Formulas  (39)  and  (44)  be  combined 
a  value  for  fs/fc  in  terms  of  p,  p'  and  d'/d  may  be  found.  These 
values  are  tabulated  in  Table  XIII. 

If  the  values  of  /',  from  (40)  be  substituted  in  (48),  it  becomes 

M 


and  making 

4Jfc+np'(*=|V^  (l-d'/d)  =N> 

we  have 


Combining  the  above  value  of  N  with  (39)  we  find  that  the  value 
of  N  depends  upon  n,  fs/fc,  p'  and  d'/d.  In  Table  XIV,  values  of 
N  are  tabulated  for  various  values  of  fs/fc,  p'  and  d'/d  when  n=  15. 

These  tables  may  be  used  in  the  investigation  of  beams  of  known 
dimensions  and  reinforcement,  for  the  purpose  of  finding  the  safe 
resisting  moment,  or  the  unit  stresses  under  given  bending  moment. 

Examples.  —  The  use  of  these  tables  will  be  best  illustrated  by 
a  few  examples. 

15.  Solve  Problem  14  (p.  187)  by  the  use  of  the  tables. 

Solution.—  As  w  =  15  and  /,  =  16,000    lb./in.2,    Table  XII  may 

be   used.    d'/e*=.09,    G=M/bd?=    "L  =  190.    From   Table 


XII,  with  /c=700,  £=190  and  d'/d  =.09,  we  find  directly  that 
p  =  .0136  and  p'  =  .0093,  from  which, 

A  =  .0136X12X22  =  3.59  in.2, 
and 

A'  -.0093X12X22  =  2.46  in.2 

16.  A  rectangular  beam  has  the  following  dimensions;  6  =  10 
inches,  d  =  18  inches,  d'  =  1.5  inches,  and  is  to  carry  a  bending  moment 
of  550,000  in.-lb.  The  safe  unit  stresses  are  600  and  14,000  lb./in.2 
for  concrete  and  steel  respectively,  n  =  15.  Find  the  areas  of  steel 
required. 

Solution.—  d'/d=  1.5/18  =  .083.  From  Table  XI  for  /,  =  14,000, 
fc  =  600,  and  d'/d  =  .083,  we  find  R  =  102,  pf  =  .0084,  fs  =  7090  lb./in.2 
substituting  these  values  in  (47)  there  results 

,,    550000-102X10X18X18 
A==-          7090X16.5-       ~  =  1-88in-2 
and  (46) 

70QO 

A  =  .0084X10X18+,^X1.88  =  2.46  in2 

IttUUU 


194  REINFORCED  CONCRETE 

17.  A  rectangular  beam  in  which  6  =  10  inches,  d=22  inches 
and  d'  =  2  inches,  is  reinforced  with  2.6  in.2  of  steel  in  tension  and 
the  same  amount  in  compression.  The  beam  carries  a  bending 
moment  of  850,000  in./lb.  What  are  the  maximum  unit  stresses 
upon  the  steel  and  concrete  respectively? 

Solution.—  p  =  p'  =  T7^7.  ™  =  .0118.    d'/d  =  .09.     For  these  values 


Table  XIII  gives  /.//«  =26.5  and  Table  XIV,  N  =  280.    Then  formula 
(49) 


/,=  627X26.5  =16620  lb./in.2 

18.  A  rectangular  beam  has  6=10  inches,  d=16  inches,  d'  =  2 
inches,  A  '  =  2.4  in.2,  A  =2.25  in.2.  If  the  safe  unit  stresses  on  steel 
and  concrete  are  16000  and  650  lb./in.2  respectively,  what  is  the  safe 
resisting  moment  for  the  beam? 


Solution. — p'=    Qx      =.015,      p=       ^       =.014,      d'/d  =  .l25. 

From  Table  XIII,  for  these  values  /,//,  =  23.0  and  Table  XIV, 
N  =  306.  If  /.  =  16,000,  fe  =  16,000/23  =  696  lb./in.2,  which  is  greater 
than  is  allowable.  The  safe  moment  will  therefore  be  that  which 
produces  a  stress  of  650  lb./in.2  in  the  concrete.  Substituting  in 
(49), 

M  =  306X650X10X16X16  =  509,184  in.-lb. 

ART.   31.    SLAB  AND   BEAM   DESIGN 

116.  Bending  Moments  and  Shears. — Structural  forms  in  which 
slabs  of  concrete  are  supported  by  T-beams  are  very  common  in  rein- 
forced concrete  structures.  In  this  type  of  construction,  the  slab 
is  commonly  made  continuous  over  the  T-beam  and  forms  the  flange 
of  the  T-beam  (see  Fig.  53),  being  built  with  the  beam  and  a  part  of 
it.  In  determining  the  bending  moments  and  shears  in  such  con- 
struction, the  loads  may  usually  be  taken  as  uniform,  and  the  slabs 
and  beams  as  fully  or  partly  continuous,  depending  upon  the  method 
of  support. 

Fully  Continuous  Beams. — If  a  slab  which  passes  over  one  or  more 
cross-beams  is  firmly  held  at  the  ends  by  being  built  into  and  tied  by 
reinforcement  to  a  wall  or  heavy  beam,  it  may  be  considered  as  fully 
continuous,  and  when  uniformly  loaded,  the  positive  moments  of 
the  middle  of  the  spans  are  -j^wl2  and  the  negative  moments  at 


SLAB  AND  BEAM  DESIGN  195 

supports  -j^wl2. .  The  shear  at  each  end  of  span  in  such  a  beam  is 
f  wl.  If  the  movable  load  covers  some  of  the  spans  leaving  others 
unloaded,  these  moments  may  be  somewhat  increased.  For  slabs 
of  this  type,  it  is  conservative  practice  to  use  -f^wl2  for  both  positive 
and  negative  bending  moments  and  \wl  for  maximum  vertical  shear. 

Supported  Ends. — The  ends  of  continuous  beams,  resting  upon 
side  walls  or  end  columns,  cannot  be  considered  as  fixed,  and  are 
to  be  taken  as  simply  supported.  Such  a  beam,  or  a  slab  the  ends  of 
which  are  not  fixed,  has  greater  positive  moments  in  the  end  spans  and 
greater  negative  moments  at  the  first  supports  from  the  ends  than 
fully  continuous  beams.  These  moments  are  usually  taken  as 
•^wl2  for  beams  of  more  than  two  spans.  The  shear  in  the  end  span 
next  the  first  support  may  be  greater  than  one-half  the  load  on  the 
span  and  should  be  taken  as  .6  wl.  For  beams  of  two  spans,  the  nega- 
tive moment  at  the  middle  support  is  taken  as  \wl 2,  and  the  positive 
moment  as  -^wl2. 

The  moments  for  continuous  beams  of  unequal  spans,  or  with 
concentrated  and  uneven  loading  should  be  carefully  determined 
for  each  individual  case. 

The  Joint  Committee  makes  the  following  recommendations  in 
its  1916  report: 

(a)  For  floor  slabs  the  bending  moments  at  center  and  at  support  should 

wl2 

be  taken  at  — -  for  both  dead  and  line  loads,  where  w  represents  the 
\2i 

load  per  linear  unit  and  I  the  span  length. 
(6)  For  beams  the  bending  moment  at  center  and  at  support  for  interior 

wlz 
spans  should  be  taken  at  — -,  and  for  end  spans  it  should  be  taken 

wl2 
at  —  for  center  and  interior  support,  for  both  dead  and  live  loads. 

(c)  In  the  case  of  beams  and  slabs  continuous  for  two  spans  only,  with 

their  ends  restrained,  the  bending  moment  both  at  the  central  support 

and  near  the  middle  of  the  span  should  be  taken  at  — -. 

(d)  At  the  ends  of  continuous  beams  the  amount  of  negative  moment 
which  will  be  developed  in  the  beam  will  depend  on  the  condition  of 
restraint  or  fixedness,  and  this  will  depend  on  the  form  of  construction 

wl2 

used.     In  the  ordinary  cases  a  moment  of  :— -  may  be  taken;     for 

lo 

small  beams  running  into  heavy  columns  this  should  be  increased, 

wl2 
but  not  to  exceed  — . 

For  spans  of  unusual  length,  or  for  spans  of  materially  unequal  length,  more 
exact  calculations  should  be  made.  Special  consideration  is  also  required  in 
the  case  of  concentrated  loads. 


196 


REINFORCED  CONCRETE 


Even  if  the  center  of  the  span  is  designed  for  a  greater  bending  moment  than 
is  called  for  by  (a)  or  (6),  the  negative  moment  at  the  support  should  not  be 
taken  as  less  than  the  values  there  given. 

117.  Loading  of  Slabs,  Beams  and  Girders. — Slabs  are  commonly 
used  as  continuous  beams  passing  over  a  number  of  T-beams,  of  which 
the  slab  forms  the  flange  as  shown  in  Fig.  53. 


"V                ^~ 

•    • 

. 

•    • 

FIG.  53.— Reinforced  Slab  and  T-Beam. 

They  are  reinforced  for  tension  in  one  direction,  perpendicular  to  the 
T-beams,  and  in  computation  are  considered  as  rectangular  beams  one 
foot  in  width.  The  T-beams  supporting  such  slabs  frequently  rest 
upon  girders,  which  are  used  to  widen  the  interval  between  columns, 
and  permit  the  T-beams  to  be  spaced  close  enough  for  economical 
design  of  slab.  The  load  upon  a  T-beam  in  such  a  system  is  uniformly 
distributed  and  consists  of  the  weight  of  a  half  span  of  the  slab  and  its 
load,  on  each  side  of  the  beam.  The  loads  upon  the  girders  are  con- 
centrated at  the  points  where  the  T-beams  cross,  but  may  usually  be 
taken  as  uniformly  distributed  without  material  error. 

Double  Reinforced  Slabs. — Slabs  of  long  span  and  nearly  square 
in  plan  may  be  supported  on  all  four  sides  and  reinforced  in  both 
directions.  It  is  not  feasible  to  make  an  accurate  analysis  of  the  dis- 
tribution of  loadings  in  such  a  slab.  When  the  length  and  width  of 
slab  are  equal,  it  is  assumed  that  the  reinforcement  in  each  direction 
carries  one-half  the  load  as  uniformly  distributed.  The  loads  carried 
by  the  mid  sections  (aaaa,  bbbb,  Fig.  54)  are,  however,  greater  than 
those  carried  by  the  sections  next  the  supports,  and  the  reinforcement 
should  be  spaced  closer  in  the  middle  than  at  the  sides.  It  is  sug- 
gested that  the  mid-half  area  (aaaa,  6666,  Fig.  80)  of  the  slab  be  con- 
sidered as  carrying  If  times  the  average  load,  and  the  side  sections 
(acca,  6cc6)  two-thirds  of  the  average  load  per  square  foot  of  slab. 

When  the  slabs  are  not  square,  the  reinforcement  parallel  to  its 
shorter  dimension  carries  the  greater  part  of  the  load.  The  Joint 
Committee  makes  the  following  recommendation  concerning  the 
division  of  the  loads  in  such  slabs: 

Floor  slabs  having  the  supports  extending  along  the  four  sides  should  be 
designed  and  reinforced  as  continuous  over  the  supports.  If  the  length  of  the 


SLAB  AND  BEAM  DESIGN 


197 


slab  exceeds  1 .5  times  its  width  the  entire  load  should  be  carried  by  transverse 
reinforcement. 

For  uniformly  distributed  loads  on  square  slabs',  one-half  the  live  and  dead 
load  may  be  used  in  the  calculations  of  moment  to  be  resisted  in  each  direction. 
For  oblong  slabs,  the  length  of  which  is  not  greater  than  one  and  one-half  times 
their  width,  the  moment  to  be  resisted  by  the  transverse  reinforcement  may  be 
found  by  using  a  proportion  of  the  live  and  dead  load  equal  to  that  given  by 

the  formula  r = =-  —  0.5,  where  I  =  length  and  6  =  breadth  of  slab.    The  longitudinal 
o 

reinforcement  should  then  be  proportioned  to  carry  the  remainder  of  the  load. 

In  placing  reinforcement  in  such  slabs  account  may  well  be  taken  of  the  fact 
that  the  bending  moment  is  greater  near  the  center  of  the  slab  than  near  the 


Jb 


FIG.  54. — Double-reinforced  Slabs. 


For  this  purpose  two-thirds  of  the  previously  calculated  moments  may 
be  assumed  as  carried  by  the  center  half  of  the  slab  and  one-third  by  the  oustide 
quarters. 

An  interesting  discussion  of  the  distribution  of  stresses  in  double 
reinforced  slabs  may  be  found  in  a  paper  by  Mr.  A.  C.  Janni  in  Trans- 
actions of  the  American  Society  of  Civil  Engineers,  1917. 

118.  Problems  in  Design. — The  use  of  the  formulas  and  tables 
which  have  been  given,  in  designing  slab  and  beams,  will  be  illustrated 
by  the  solution  of  a  few  problems.  In  these  examples,  the  working 
stresses  recommended  by  the  Joint  Committee  for  2000  pounds  con- 
crete will  be  used. 

Example  19. — A  concrete  slab  is  to  be  supported  by  T-beams  6 
feet  apart  c.  to  c.,  and  to  carry  a  live  load  of  250  pounds  per  square 


198 


REINFORCED  CONCRETE 


foot.     The  T-beams  have  a  clear  span  of  17  J  feet  and  are  built  into 
brick  walls  at  the  ends.     Design  the  slab  and  beams. 

Solution.  —  Assume  the  weight  of  slab  as  50  pounds  per  square 
foot,  giving  a  total  load  of  300  pounds  per  linear  foot  for  a  section  of 
slab  12  inches  wide.  Taking  the  slab  as  fully  continuous. 

.,    wl2    300X6X6X12 

—  =  10,800  m.-lb. 


i  - 


i  - 


From  Table  VII,  for  /s=  16,000  and  /<•  =  650,  #  =  108,  p  =  .0078  and 
j=.874.  Formula  (9)  gives  12d2  =  10,800/1  08  =100,  and  d  =  2.9 
inches,  use  3  inches.  A  =  p6d  =  3Xl2X.0078  =  .277  in.2  From 
Table  XV  (p.  199),  we  select  f-inch  round  bars  spaced  4.5  inches 
apart,  A  =  .29  in.2 

If  concrete  extends  f  inch  below  steel,  the  thickness  of  slab  is 
3J  inches,  and  the  weight  of  slab  is  150X3.75/12  =  47  pounds  per 
square  foot,  which  agrees  with  the  assumed  load. 


FIG.  55. — T-Beam  Design. 

Reinforcement  for  negative  moment  over  the  supports  should  be 
the  same  as  for  positive  moment  at  mid-span,  and  will  be  provided  by 
turning  up  every  alternate  bar  at  the  quarter  point  on  each  side  of  the 
support  and  continuing  them  over  the  support  to  the  one-third  point. 
Transverse  reinforcement  to  prevent  cracks  will  be  provided  by  using 
f-inch  bars  spaced  12  inches  apart. 

Unit  shear  at  ends  of  slab, 

V          300X3 


bjd     12  X. 874X3 


28.61b./in.2 


No  diagonal  tension  reinforcement  is  necessary. 

T-beam. — Assuming  the  weight  of  the  web  of  the  T-beam  as  150 
pounds  per  linear  foot,  the  total  load  on  the  T-beam  is  6(250+47) 
+  150=1930  pounds  per  linear  foot.  Taking  the  bearing  upon  the 
wall  as  6  inches  the  effective  length  of  T-beam  between  centers  of 
bearings  is  17.5+.5=18  feet. 


SLAB  AND  BEAM  DESIGN 


199 


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200  REINFORCED  CONCRETE 


The   maximum   shear   7=1930x9  =  17370   pounds.     The  area 

V     17370 

uired  for  shear,   assuming  j  =  f,  b'd  =  —  =  -^^-=165.  in.2 

vj       luo 

For  6'  =8,  d=2l  or  for  6'  =9,  d=18.5.    Take  6'  =9,  and  (2  =  18.5. 


Width  of  flange  6  =  2X6X3f  +9  =  54  inches,  and  by  (31) 
~     M  923400  d 


from  Diagram  I,  /c  =  430  lb./in.2,  and  p  =  .0035,  then 
A  =pbd  =  .  0035X54X18.5  =  3.50  in.2, 

and  from  Table  X,  six  f-inch  round  bars  in  two  rows,  2  inches  c.  to  c., 
spaced  2.75  inches  apart  in  the  rows  and  1.75  inches  from  side  of 
web.  4=3.61  in.2 

As  the  ends  of  the  beam  are  built  into  the  walls,  some  negative 
moment  may  be  developed  at  the  supports,  which  might  cause  cracks 
to  occur  unless  reinforced.  The  upper  layer  of  reinforcement  will 
therefore  be  turned  up,  two  rods  at  the  quarter  point  and  the  other 
midway  between  the  quarter  point  and  support,  and  extend  to  the  end 
of  the  beam  (see  Fig.  55). 

If  the  concrete  extend  2  inches  below  the  steel,  the  weight  of  web 
below  the  slab  is  9(18.5+3-  3.75)  X  150/144  =166  pounds  per  linear 
foot.  This  is  a  little  greater  than  the  assumed  value,  but  would  add 
less  than  1  per  cent  to  the  total  load  and  need  not  be  redesigned. 
For  the  three  bars  in  bottom  of  beam  at  the  support.  Table  X  gives 
20  =  3X2.75  =  8.25,  and  the  unit  bond  stress  u=  b  'v/2o=  9X120/8.25 
=  131  lb./in.2  This  is  too  great  for  safety,  and  the  bars  should  be 
bent  into  hooks  at  the  ends. 

v  is  120  lb./in.2  at  the  supports,  and  diagonal  tension  reinforce- 
ment is  needed  where  v  is  more  than  40  lb./in.2  Stirrups  will  be 
needed  for  two-thirds  of  the  distance  from  the  support  to  the  mid- 
span,  or  6  feet.  If  the  stirrups  be  spaced  s  =  d/2  =  9  inches  apart, 
eight  stirrups  will  be  needed  at  each  end  of  the  beam.  For  the 
stirrups  next  the  support  (34) 

A      vb's     120X9X9      q    .    2 
A'  =  ~2f-=  2X16000  ='31in> 

Two  J-inch  round  bars,  bent  as  shown  (Fig.  55)  may  be  used  for  the 
first  four  stirrups,  and  f-inch  bars  for  the  four  nearer  the  middle  of 
the  beam. 


SLAB  AND  BEAM  DESIGN  201 

Example  20.  —  A  reinforced  concrete  slab,  to  carry  a  live  load  of 
200  pounds  per  square  foot,  is  to  rest  upon  a  series  of  T-beams  5  feet 
apart  c.  to  c.  The  T-beams  are  to  be  continuous  for  three  spans  over 
girders  15  feet  c.  to  c.  The  girders  are  supported  by  walls  at  the 
ends  and  have  a  span  of  20  feet.  Design  the  slab  and  beams. 

Solution.  —  Assume  the  weight  of  slab  at  40  pounds  per  square 

foot;     then   M  =  24QX5*5X12 


#  =  108,  p  =  .0078,  j  =  .874,  12^  =  6000/108  =  55.5  and  d=2.15, 
Take  d  =  2.25  in.  A  =  2.25  X  12  X  .0078  =  .21  in.2 

If  concrete  extend  f-inch  below  steel,  the  total  depth  of  slab  is 
3  inches,  and  weight  of  slab  is  150XA  =  37.5  pounds  per  square  foot. 

From  Table  XV  j^-inch  round  bars  spaced  4  inches  apart  give 
A  =  .23.  in.2  Negative  moment  at  supports  will  be  provided  for  by 
bending  these  up  at  the  quarter  points.  For  lateral  reinforcement 
to  prevent  cracks,  ^-inch  round  bars  spaced  12  inches  c.  to  c.  will  be 
used. 

T-beams.  —  Assuming  weight  of  web  of  T-beam  as  125  pounds  per 
linear  foot,  load  upon  T-beam  is  5(200+40)  +  125=  1325  pounds  per 
linear  foot  and  total  span  load  is  1325  X  15=  19,875  pounds. 

Maximum  shear  in  end  span  next  girder  is  V  =19,875  X.6  =  11,- 
925  pounds,  and  6^=7/^=11,925/105=113  in.2  7X16  or  8X14 
might  be  used.  Try  7X16,  then  M=Wl/10=  19,875X15X12/10  = 
357,750  in.-lb.  Taking  overhang  of  flange  as  six  times  its  depth,  6  = 
2X6X3+7  =  43  inches  and  Formula  (31) 


From  diagram  7,  /c  =  325  lb./in.2  and  p=.0024.  ^1  =  1.65  in.2 
Table  X,  six  f-inch  round  bars,  A  =  1.84  in.2  in  two  rows,  If  inches 
apart  and  spaced  2  inches  c.  to  c.  and  1.5  inches  from  side  of  web. 

If  concrete  extends  2  inches  below  steel,  the  weight  of  web  below 
slab  is  7X16X150/144=117  pounds  per  linear  foot,  which  is  within 
the  assumed  load. 

The  negative  moment  at  crossing  of  girder  is  equal  to  the  posi- 
tive moment  already  found.  Turn  up  the  upper  row  of  bars  on  each 
side  to  provide  for  tension  at  top  of  beam  and  run  the  lower  ones 
through  at  bottom  to  provide  compression  reinforcement  as  shown 
in  Fig.  56.  We  now  have  a  beam  with  compression  reinforcement, 
in  which  6  =  7,  d  =  16,  d'  =  3,  A=A'=1.84,  p=p'=  1.84/112  =  .0164, 


202 


REINFORCED  CONCRETE 


Formula  (48)  gives  G  =       = 


=  200,  and   Table   XII, 


for/5=16000,  /c  =  650,  £  =  200,  and  d'/d  =  .!S,  we  find  that  p  =  .0139 
and  p'  =  .0219  are  required.  The  area  of  steel  in  compression 
(p  .0164)  is  not  sufficient  and  we  must  either  increase  the  area  of 
compression  steel  in  the  bottom  of  beam  or  increase  the  area  of 
concrete  section  over  the  support.  Try  making  d  —  17  inches.  Then 


Now  from  Table  XII,  we  find  that  p  =  .0123  and  p'  =  .0156  are 
required.     The  reinforcement  is  now  sufficient  and  we  will  increase 


FIG.  56.— T-Beam  and  Girder. 

the  depth  to  17  inches  at  the  girder,  sloping  the  haunches  as  shown 
in  Fig.  56. 

Diagonal  Tension. — Assuming  J  as  .85,  the  maximum  unit  shear 


—=  =  118  lb./in.2     If  stirrups  be  spaced 


next  the  girder  is  v  =         85  x  17 
8  inches  apart,  the  area  required  for  the  end  stirrups  is  (34) 

118X7X8 


2X16000 


=  .21  in.2 


Two  f-inch  bars  will  answer,  or  a  f-inch  bar  bent  to  U-shape  around 
horizontal  reinforcement.  Stirrups  will  be  needed  to  6  feet  from 
girder  and  4  feet  from  end  support  in  the  end  spans  and  5  feet  from 
girder  on  each  end  of  the  middle  span. 

Girders. — The  girders  are  simple  rectangular  beams  carrying  three 
concentrated  loads  at  the  middle  and  quarter  points.  Each  load  is 
1.1  times  a  span  load  of  the  T-beam,  or  1.1X19875  =  21862  pounds; 
assuming  that  the  girder  weighs  800  pounds  per  linear  foot,  the 
reaction  or  shear  at  the  support  is  1.5X21862+800X10=40793 
pounds  and  the  maximum  bending  moment  M  =  40,793  X  (120— 
29,862)  X  60  =  3,103,440  in.-lb.  bd2  =  3, 103,440/108  =  28,735.  For 


SLAB  AND  BEAM  DESIGN  203 

6  =  20,  d=38;  for  6  =  18,  d=40.  Try  6  =  18,  d  =  40;  then  A  =  .0078X 
18X40  =  5.61  in.2.  Ten  f-inch  square  bars  (4  =  5.62)  placed  in  two 
rows  If  inches  c.  to  c.,  six  bars  in  lower  and  four  in  upper  layer 
(Fig.  56).  If  concrete  extend  2}  inches  below  center  of  lower  layer 
of  steel,  the  beam  is  43  inches  deep  and  weighs  18  X  43  X  150/144  =  806 
pounds  per  linear  foot,  which  agrees  with  the  assumed  weight. 

40793 
The  maximum  unit  shear  v  =  Q7/1x//m  =65  lb./in.2     Diag- 


onal  tension  reinforcement  will  be  needed  from  support  to  first  load 
(60  inches)  .  This  may  be  supplied  by  bending  up  horizontal  steel. 
The  bending  moment  at  first  load  is 

40,793  X  60  -4000X30  =  2,327,580  in.-lb. 

This  is  about  three-fourths  of  the  moment  at  the  middle  and  two 
bars  may  be  bent  up  at  this  point.  For  two  bars  4^  =  1.12  in.2, 
and  Formula  (15) 

AdfsV2     1.12X16000X1.4 
s  =  -^-r  —  =  -  grvxio  -  =21.5  inches. 
vb  65  X  18 

Turn  up  pairs  of  bars  at  20,  40  and  60  inches  from  support. 
The  bond  stress  on  four  horizontal  bars  at  end  of  beam  is 

bv     18X65     _„    ,. 


This  is  rather  large  unless  deformed  bars  are  used,  and  bars  should 
be  bent  into  hooks  at  ends. 

Example  21.  —  A  reinforced  concrete  slab,  divided  into  panels 
12  ft.X!4  feet,  by  T-beam  supports  is  to  carry  a  live  load  of  150 
pounds  per  square  foot.  The  T-beams  are  supported  by  columns 
at  the  corners  of  the  panels;  their  ends  resting  upon  side  walls. 
Design  the  slab  and  beams. 

Solution.  —  Assume  the  weight  of  slab  at  70  pounds  per  square 
foot.  The  proportion  of  load  carried  by  the  12-foot  span  is  14/12 
—0.5  =  .67  (see  Section  117).  The  load  on  the  slab  in  the  12-foot 
length  is  (150+70)  X.  67  =147  Ib.  per  square  foot  and  in  the  14-foot 
length  220  X.  34  =  75  pounds  per  square  foot.  If  4/3  of  the  average 
load  per  square  foot  be  borne  by  the  mid-section,  the  load  to  be 
carried  by  a  12-inch  width  will  be  147X4/3  =  196  pounds  per 
linear  foot. 


204  REINFORCED  CONCRETE 

12d2  =  28224/108  =  261  and  d  =  4.75  inches.  If  the  concrete  extend 
f  inch  below  steel,  the  total  depth  of  slab  will  be  5.5  inches  and  the 
weight  of  slab  150X5.5/12  =  69  pounds  per  square  foot,  as  assumed. 

A  =  .0078X12X4.75  =  .44  in.2  From  Table  XV,  f-inch  square 
bars  spaced  3.5  inch  c.  to  c.  may  be  used. 

Alternate  bars  in  each  span  will  be  turned  up  at  the  quarter 
points  for  negative  shear  at  the  supports. 

The  side-sections  of  the  shorter  span  will  carry  one-half  the 
moment  of  the  mid-sections,  and  will  need  about  one-half  the  rein- 
forcement. We  will  space  the  f-inch  bars  6  inches  apart  for  the 
side  sections. 

For  the  longer  span  (14  feet)  the  load  upon  the  mid-section  will 
be  75X4/3  =  100  pounds  per  linear  foot,  and  the  bending  moment 

,,     100X14X14X12     1ftnAA   .     1U       T,  .  , 

M  —  -    —  -=  —       —  =  19,600   in.-lb.      If   we   place   the   reinf  orce- 


ment  in  the  14-foot  direction  on  top  of  that  in  the  shorter  span,  the 
effective  depth  will  be  about  J-inch  less,  or  d  =  4.75—  0.5  =4.25  inches, 

and  R==  ^2  =  ^x^25X4:  25  =  86.     From  Table  VII,  we  find  that 


if  /s=16,000  and  #  =  86,  p  =  .006  and  /c  =  565  lb./in.2  A  =  .006X12 
X4.25  =  .306  in.2  and  Table  XV  gives  f-inch  round  bars  spaced 
4  inches  apart,  A  =  .33  in.2  Use  these  for  mid-half  of  slab  and  bars 
of  the  same  size  spaced  7  inches  apart  for  the  side-sections. 

T  -Beams.  —  Assuming  the  longer  T-beam  to  weigh  250  pounds 
per  linear  foot,  the  total  load  will  be  196X12X14+250X14=36,428 
pounds.  The  maximum  shear  will  be  V  =  36,428  X  .6  =  21,857  pounds 
and  section  needed  for  shear  &'d  =  21,857/105  =  208  in.2  Try 
V  =  10,  d  =  2l  inches. 

The  load  at  the  middle  of  the  beam  is  greater  than  that  at  the 
ends;  this  somewhat  increases  the  moment,  but  the  error  will  not 
be  more  than  about  2  per  cent  if  the  load  be  taken  as  uniformly 
distributed. 

ul     35428X14X12  . 

M  =—  =  —     —  —  —     —  =  611,990  in.-lb. 

Taking  the  width  of  flange  as  one-fourth  the  length  of  beam 
6=45  in. 

M          611990  d/*- 

~ 


From  Diagram  I,  we  find  that  the  neutral  axis  is  in  the  flange 
and  the  beam  should  be  designed  as  a  rectangular  section. 

and 


SLAB  AND  BEAM  DESIGN  205 

#  =  29,  we  see  that  fe  will  be  less  than  350  lb./in.2  and  the  steel 
needed  is  p  =  .0021  (p  =  7#/100QOO  approximately)  or  A  =  .0021X45 
X  20  =1.89  in.2  Four  fj-inch  square  bars  may  be  used.  Two  of 
these  bars  to  be  turned  up  at  the  quarter  point  on  each  side  of  the 
support  to  provide  for  tension  due  to  negative  moment. 

We  now  have  at  the  support  a  double  reinforced  beam  in  which 
6  =  10  inches,  d  =  21  inches,  A  =  A  '  =  1.89  in.2,  p  =  p'  =  1.89/210  =  .0090, 

dr  =  2  inches,  d'/d  =  .095  and  G  =  in!^o???01  =  136-    From  Table  XII> 

lUX^l  X^l 

for  /,=  16,000,  fe  =  650,  £=136  and  d'/d  =.095  we  find  that  p  =  0096 
and  p'  =  .0042  are  required.  The  reinforcement  for  tension  is  a 
little  small,  but  as  the  beam  will  be  strengthened  by  the  slab  rein- 
forcement parallel  to  it,  the  j^-inch  bars  will  probably  be  ample. 

Diagonal  tension  reinforcement  will  be  needed  for  5  feet  from 
the  supports.  If  stirrups  be  spaced  9  inches  apart,  seven  stirrups 
will  be  needed.  The  first  stirrup  will  require 


A  ___  QA  .    2 
A'~2/s~   2X16000   = 

^-inch  round  bars  bent  to  U-shape  will  answer  for  the  first  three 
stirrups,  the  four  next  the  middle  of  the  beam  may  be  f-inch. 

The  loads  upon  the  shorter  beams,  assuming  the  beam  to  weigh 
150  pounds  per  foot,  are  100X14X12+150X12  =  18600  pounds. 
The  maximum  shear  is  18600  X.6  =  11160  pounds.  6^=11160/105 
=  106.  A  section  7  inches  X  16  inches  might  be  used,  but  assuming 
that  the  depth  must  be  the  same  as  for  the  longer  beams,  we  may 
use  7  inches  X  21  inches.  Then 

M==  18600  XJ2X  12  =  26784Q  in  _lb  ^  and  6  =  //4  =  36  inches 

267840 
As  before,  the  neutral  axis  is  in  the  flange,  # 


and  Table  VII,  fe  will  be  small  and  p  =  .0012.  A  =  .0012X36X21 
=  0.90  in.2  Three  f-inch  round  bars  will  be  used.  Part  of  these 
bars  will  be  turned  up,  two  on  one  side  and  one  on  the  other  of  each 
support  to  provide  for  tension  due  to  negative  moment.  Then 


and  from  Table  XII  we  find  that  no  compression  steel  is  necessary. 

Maximum   unit   shear,   v=  Q^K  =  ^  lb./in.2     Diagonal 

i  X^l  X  .  01  O 


206 


REINFORCED  CONCRETE 


tension  reinforcement  is  needed  72X47/87=40  inches  from  support. 
Spacing  stirrups  10  inches  apart,  for  end  stirrups 

87X10X10 


Ac      2X16000 
Use  f-inch  square  bars  bent  to  U-shape. 


.27  in.2 


ART.   32.     CONCRETE   COLUMNS 

119.  Plain  Concrete  Columns. — The  strength  of  plain  concrete  in 
compression  has  been  discussed  in  Section  94.  The  failure  of  a  short 
block  under  compression  occurs  through  lateral  expansion  and  the 
shearing  of  the  material  on  surfaces  making  angles  of  about  30° 
with  the  line  of  pressure  as  shown  in  Fig.  57  (a).  As  the  height  of 
block  becomes  greater  in  proportion  to  its  diameter,  the  resistance  of 
the  concrete  becomes  less  certain  and  plain  columns  in  which  the 
length  is  more  than  four  times  the  height  frequently  fail  by  shearing 
diagonally  across  the  column  as  shown  in  Fig.  57  (6).  This  usually 


T 

(a)  (5) 

FIG.  57. — Crushing  of  Concrete  Columns. 

occurs  where  the  concrete  is  of  good  quality  and  shows  high  crushing 
strength.  Weaker  concrete  usually  fails  by  local  crushing. 

Columns  in  which  the  lengths  are  more  than  six  or  eight  times  the 
diameters  are  usually  reinforced.  The  Joint  Committee  recommends 
that  all  columns  more  than  four  diameters  be  reinforced,  and  that 
the  stress  on  plain  columns  be  limited  to  22.5  per  cent  of  the  ultimate 
crushing  strength  of  the  concrete. 

The  use  of  concrete  rich  in  cement  is  nearly  always  advisable 
in  the  construction  of  columns,  on  account  of  the  greater  reliability 
of  such  concrete,  as  well  as  because  of  the  economy  of  reduced  section 


CONCRETE  COLUMNS  207 

allowable  with  rich  concrete.  In  reinforced  columns,  concrete  of 
high  compressive  strength  also  admits  of  more  economical  use  of  steel, 
through  employing  higher  unit  stresses  than  are  admissible  with  less 
rich  concrete.  Concrete  less  rich  than  1  to  6  (2000  pounds)  mixtures 
(see  Section  94)  is  undesirable  in  column  work  and  richer  mixtures 
are  commonly  preferable. 

120.  Longitudinal  Reinforcement.  —  Longitudinal  bars  in  the 
corners  of  square  columns,  or  near  the  exterior  surfaces  of  round 
columns,  diminish  the  uncertainty  of  action  of  the  columns  through 
preventing  the  material  yielding  at  points  of  local  weakness.  Such 
reinforcement  should  always  be  stayed  by  light  band  reinforcement 
at  frequent  intervals  as  shown  in  Fig.  58  (a).  This  will  prevent  the 
longitudinal  bars  breaking  away  from  the  column  through  bending 
when  loaded. 

When  a  column  containing  longitudinal  steel  is  loaded,  the  con- 
crete and  steel  are  shortened  by  the  compression  to  the  same  extent 
and  the  stress  carried  by  each  material  is  proportional  to  its  modulus 
of  elasticity. 

Let    A  =  cross-section  of  column  ; 
AS  =  cross-section  of  steel; 
p  =  steel  ratio  =  As/  A  ; 
n  =  ratio  of  moduli  of  elasticity  =  ES/EC', 
P  =  total  load  on  columns  ; 
fc  =  unit  compression  on  concrete  ; 
/s  =  unit  compression  on  steel  =  nfc. 

The  total  area  of  concrete  is  A(l  —  p),  and 

P=feA(l-p)+f.A.=fe(A-pA)+fcnpA, 
or 

.      ..   .     ;-   .     .     .  ':.     .     (50) 


The  Joint  Committee  recommends  the  following  working  stresses  : 

(a)  Columns  with  longitudinal  reinforcement  to  the  extent  of  not  less 
than  1  per  cent  and  not  more  than  4  per  cent,  and  with  lateral  ties 
of  not  less  than  j  inch  in  diameter  12  inches  apart,  nor  more  than 
16  diameters  of  the  longitudinal  bar:  the  unit  stress  recommended 
for  axial  compression,  on  concrete  piers  having  a  length  not  more 
than  four  diameters. 

The  Committee  also  recommends  that  the  ratio  of  unsupported  length 
of  column  to  its  least  width  be  limited  to  15,  and  that  the  hoops  or 
bands  are  not  to  be  counted  on  directly  as  adding  to  the  strength 
of  the  column. 


208 


REINFORCED  CONCRETE 


In  Formula  (50),  if  we  let  Z=l  +  (n—  l)p  =  r-r,  and   tabulate 

hA 

values  of  Z  (see  Table  XVI)  in  terms  of  n  and  p,  the  computation 
of  columns  of  this  type  becomes  very  simple. 

TABLE  XVI.— COLUMNS  WITH  LONGITUDINAL  REINFORCEMENT 

P 

Values  of  Z  =  — ,  in  Terms  of  n  and  p 
fcA 


P 

n  =  10 

n  =  12 

n  =  15 

P 

n  =  10 

n  =  12 

n  =  15 

0.006 

1.054 

.066 

1.084 

0.021 

.189 

.231 

1.294 

0.007 

1.063 

.077 

1.098 

0.022 

.198 

.242 

1.308 

0.008 

1.072 

.088 

1.112 

0.023 

.207 

.253 

1.322 

0.009 

1.081 

.099 

1.126 

0.024 

.216 

.264 

1.336 

0.010 

1.090 

.110 

I.f40 

0.025 

.225 

.275 

1.350 

0.011 

1.099 

.121 

1.154 

0.026 

.234 

.286 

.364 

0.012 

1.108 

.132 

1.168 

0.027 

.243 

.297 

.378 

0.013 

1.117 

.143 

1.182 

0.028 

.252 

.308 

.392 

0.014 

1.126 

.154 

1.196 

0.029 

.261 

.319 

.406 

0.015 

1.135 

.165 

1.210 

0.030 

.270 

.330 

.420 

0.016 

1.144 

.176 

1.224 

0.032 

.288 

.352 

.448 

0.017 

1.153 

.187 

1.238 

0.034 

.306 

.374 

.476 

0.018 

1.162 

.198 

1.252 

0.036 

1.324 

.396 

.504 

0.019 

1.171 

.209 

1.266 

0.038 

1.342 

.418 

.532 

0.020 

1.180 

.220 

1.280 

0.040 

1.360 

.440 

.560 

Example  22. — A  square  column  is  to  carry  a  load  of  95,000  pounds, 
and  to  be  reinforced  with  2  per  cent  of  longitudinal  steel.  If  fc =450 
Ib./in.  and  n=15,  find  dimensions  for  column  and  steel. 

Solution.— From  Table  XVI,  for  ft  =15  and  p  =  .020,  we  find 

Z=  1.280.     Then  A  =  ^-~=165,   and   side  of   column    =13  inches. 

A,=  . 020X165  =  3.30  in.2  From  Table  X,  four  ^f-inch  square  bars 
may  be  used,  As  =  3.52  inches. 

If  1  to  3  concrete  of  3000  pounds  compressive  strength  (see  Section 
94)  were  used  in  the  above  problem,  we  would  have  fc  =  675,  n=10, 
7  =  1.18,  A  =  119  in.2  and  As  =  2.38  in.2  The  quantities  of  materials 
required  would  be  reduced  about  25  per  cent,  while  the  proportion  of 
cement  in  the  concrete  would  be  about  doubled. 

Example  23.  —  A  column  14  in.Xl4  in.  section  is  to  carry  a 
load  of  130000  pounds.  If  /c  =  450  and  n=15  find  area  of  steel 
required. 


CONCRETE  COLUMNS 


209 


Solution. — Z 


130000          1  .„. 
IT-TV;- =  1.474 


and  from  Table  XVI, 


450X14X14 

p  =  .034.  Then  As=. 034X14X14  =  6.66  in.2  This  might  be  four 
l|-inch  round  bars  at  the  corners  (As  =  7.07),  or  eight  ff-inch  square 
bars  at  corners  and  middle  of  sides  (As  =  7.03),  or  four  IJ-inch  round 
bars  at  corners  and  four  f-inch  round  bars  at  middle  of  sides. 
(As  =  6.68in.2). 

The  Joint  Committee  recommends  a  minimum  of  1  per  cent  of 
longitudinal  steel  for  columns  of  more  than  four  diameters  in  length. 
This  gives  rigidity  to  the  column,  and  security  against  local  yielding 
in  the  concrete.  High  percentages  of  longitudinal  steel  are  not 


(a) 


ft) 

FIG.  58. — Reinforced  Concrete  Columns. 


usually  economical,  because  of  the  greater  cost  of  steel  as  compared 
with  concrete  for  resisting  compression,  particularly  when  the  stresses 
in  the  steel  are  limited  by  those  in  the  concrete. 

When  the  concrete  is  used  for  fireproofing,  the  steel  should  be 
covered  by  at  least  2  inches  of  concrete,  and  about  1  \  inches  of  con- 
crete on  the  exterior  of  the  column  should  not  be  considered  in  deter- 
mining the  strength  of  the  column. 

121.  Columns  with  Hooped  Reinforcement. — As  shown  in  Section 
95,  the  failure  of  concrete  under  compression  commonly  occurs 
through  shearing  due  to  lateral  expansion.  If  the  concrete  in  the 
column  be  held  by  band  or  spiral  steel  (see  Fig.  58  (6) )  from  yielding  to 


210  REINFORCED  CONCRETE 

lateral  expansion,  the  resistance  to  crushing  will  be  materially  in- 
creased. Such  reinforcement  is  either  formed  of  steel  bars  bent  to 
form  a  spiral  or  bands  of  steel  spaced  at  a  uniform  distance  apart, 
but  in  either  case,  the  bands  should  not  be  spaced  more  than  about 
one-sixth  of  the  diameter  of  the  column  apart,  and  must  be  held  in 
place  by  longitudinal  spacing  bars. 

Experiments  upon  columns  with  hooped  reinforcement  indicate 
that  the  deflections  under  working  loads  are  not  decreased  by  the 
reinforcement,  but  the  ultimate  strength  is  considerably  increased,  as 
compared  with  columns  without  such  reinforcement.  When  hcoped 
reinforcement  is  used,  it  is  usual  to  allow  a  larger  unit  stress  than  for 
plain  columns,  or  those  with  longitudinal  reinforcement  only.  The 
effective  area  of  the  column  is  that  inside  the  reinforcement.  The 
concrete  outside  the  hooping  is  stripped  off  when  a  stress  is  reached  at 
which  plain  concrete  would  fail. 

Hooped  reinforcement  prevents  crushing  of  the  concrete  until  a 
load  is  reached  which  stresses  the  steel  to  its  yield  point,  but  does  not 
stiffen  the  column  longitudinally,  and  columns  so  reinforced  fre- 
quently fail  by  bending.  This  reinforcement  is  commonly  combined 
with  longitudinal  steel  as  shown  in  Fig.  58  (c).  The  longitudinal 
steel  serves  to  stiffen  the  column  against  bending,  and  makes  the 
hooping  more  effective.  In  general,  it  is  not  advisable  to  use  hooped 
reinforcement  without  longitudinal  steel,  as  the  same  amount  of 
steel  would  be  more  effective  in  strengthening  the  column  if  used  as 
longitudinal  steel. 

Experiments  indicate  that  about  1  per  cent  of  steel  in  closely 
spaced  hooping  is  sufficient  to  resist  lateral  expansion  and  give  in- 
creased strength  in  compression.  Larger  amounts  of  steel  do  not 
materially  increase  the  resistance.  The  Joint  Committee  makes  the 
following  recommendations : 

(6)  Columns  reinforced  with  not  less  than  1  per  cent  and  not  more  than 
4  per  cent  of  longitudinal  bars  and  with  circular  hoops  or  spirals  not 
less  than  1  per  cent  of  the  volume  of  the  concrete  and  as  hereinafter 
specified:  a  unit  stress  55  per  cent  higher  than  given  for  (a),  provided 
the  ratio  of  unsupported  length  of  column  to  diameter  of  the  hooped 
core  is  not  more  than  10. 

The  foregoing  recommendations  are  based  on  the  following  conditions: 

It  is  recommended  that  the  minimum  size  of  columns  to  which  the  working 
stresses  may  be  applied  be  12  inches  out  to  out. 

In  all  cases  longitudinal  reinforcement  is  assumed  to  carry  its  proportion  of 
stress.  The  hoops  or  bands  are  not  to  be  counted  on  directly  as  adding  to  the 
strength  of  the  column. 

Longitudinal  reinforcement  bars  should  be  maintained  straight,  and  should 


CONCRETE  COLUMNS  211 

have  sufficient  lateral  support  to  be  securely  held  in  place  until  the  concrete 
has  set. 

Where  hooping  is  used,  the  total  amount  of  such  reinforcement  shall  be  not 
less  than  1  per  cent  of  the  volume  of  the  column,  enclosed.  The  clear  spacing 
of  such  hooping  shall  be  not  greater  than  one-sixth  the  diameter  of  the  enclosed 
column  and  preferably  not  greater  than  one-tenth,  and  in  no  case  more  than  2 
inches.  Hooping  is  to  be  circular  and  the  ends  of  bands  must  be  united  in  such 
a  way  as  to  develop  their  full  strength.  Adequate  means  must  be  provided 
to  hold  bands  or  hoops  in  place  so  as  to  form  a  column,  the  core  of  which 
shall  be  straight  and  well  centered.  The  strength  of  hooped  columns  depends 
very  much  upon  the  ratio  of  length  to  diameter  of  hooped  core,  and  the  strength 
due  to  hooping  decreases  rapidly  as  this  ratio  increases  beyond  five.  The  work- 
ing stresses  recommended  are  for  hooped  columns  with  a  length  of  not  more 
than  ten  diameters  of  the  hooped  core. 

The  Committee  has  no  recommendation  to  make  for  a  formula  for  working 
stresses  for  columns  longer  than  ten  diameters. 

Let   d  =  effective  diameter  of  column  in  inches; 

a  =  area  of  the  steel  bar  to  be  used,  in  square  inches; 
s  =  longitudinal  spacing  of  the  bands  or  spirals,  in  inches; 
p  =  ratio  of  steel  to  concrete  in  column. 
Then 

a  =  pds/4: 
or 

s=4a/pd    .........     (51) 

From  this  we  may  obtain  the  size  of  bars  necessary  for  steel  of  re- 
quired spacing,  or  the  spacing  required  for  bars  of  given  size. 

Example  24.  —  A  concrete  column  is  to  carry  a  load  of  225,000 
pounds  and  be  reinforced  with  1  per  cent  of  spiral  steel  and  2  per  cent 
of  longitudinal  steel.  Using  the  stresses  recommended  by  the 
Joint  Committee  for  concrete  of  2000  pounds  compressive  strength, 
find  dimensions  for  concrete  and  steel. 

Solution.  —  Without  hooped  reinforcement,  the  value  of  fc  would 
be  limited  to  22.5  per  cent  of  the  compressive  strength,  or  450  lb./  in. 
This  may  be  increased  55  per  cent  when  spiral  reinforcement  is  used 
or  /c  =  700  lb./in.2 

Using  Table  XVI,  for  p  =  .02  and  rc  =  15,  Z=1.28,  from  which 

P        225000 

0   =251  in.2,  and  diameter  of  column  is  18  inches. 


Longitudinal  steel,  As=.  02X251  =  5.02  in.2  From  Table  X  we  see 
that  five  1-inch  square  bars,  spaced  about  11  inches  apart  about 
the  circumference  of  the  column,  or  nine  f-inch  square  bars  spaced 
about  6  inches  apart  may  be  used.  For  the  spiral  steel,  we  find 
from  (51)  that  if  the  spacing  be  made  2|  inches,  a  =  .OlXl8X2J/4 
=  .112  in.2,  and  f-inch  round  bars  may  be  used. 


212  REINFORCED  CONCRETE 

122.  Eccentrically  Loaded  Columns.  —  When  the  center  of  gravity 
of  the  load  upon  a  column  does  not  coincide  with  the  gravity  axis  of 
the  column,  bending  stresses  are  produced  which  must  be  taken  into 
account  in  designing  the  column.  In  some  cases,  lateral  forces  may 
be  acting  upon  a  column,  producing  bending  moments,  as  in  wall 
columns  carrying  the  ends  of  beams  which  are  firmly  attached  to  the 
columns.  When  these  conditions  exist,  the  maximum  unit  com- 
pression due  to  both  direct  thrust  and  bending  moment  at  any  sec- 
tion must  not  exceed  the  safe  values  for  the  concrete,  and  any  tensions 
which  may  occur  must  be  taken  by  proper  reinforcement. 

Let  Fig.  59  represent  the  section  of  a  column  under  eccentric 
load. 

A  =  area  of  section  of  column; 
As  =  area  of  longitudinal  steel  hi  section; 
P=  longitudinal  load  on  column; 
e  =  eccentricity  of  load  ; 

Ic  —  moment  of  inertia  of  section  about  its  gravity  axis; 
Is  =  moment  of  inertia  of  steel  area  about  same  axis; 

u  —  distance  gravity  axis  to  most  remote  edge  of  section  ; 
M—  bending  moment  on  section,  Pe; 
fc  =  maximum  unit  compression  on  concrete; 
f'c  =  minimum  unit  compression  on  concrete. 

/c  =  is  made  up  of  two  parts  —  that  due  to  direct  thrust  and  that 
due  to  bending  moment,  and  is 

f_  P  ,  MU  /KIN 

7'    A+(n-l)A^/,+(n-l)// 

and 


Mu 


When  the  stress  due  to  moment  is  greater  than  that  due  to  direct 
thrust,  fc  becomes  negative,  showing  the  stress  to  be  tension. 
Tensions  in  columns,  if  occurring  at  all,  should  be  very  small  and 
need  not  be  specially  provided  for.  The  stresses  in  steel  are  always 
less  than  nfc,  and  therefore  within  safe  limits. 

If  the  section  is  symmetrical  about  its  gravity  axis,   u  =  d/2t 

bd3 

and  for  rectangular  sections,    Ic  =  -^r  and  Is  =  Asds2/4,  in  which  ds 

\2i 

is  distance  between  centers  of  steel  on  the  two  sides  of  column.  For 
circular  sections,  Ic  =  .049d4  and  Is  =  .125Asds2,  where  d  is  the  diameter 
of  the  column  and  ds  is  diameter  of  the  circle  containing  the  centers  oi 
the  steel  bars. 


CONCRETE  COLUMNS 


213 


Example  25. — A  wall  column,  12X16  inches  in  section,  carries 
the  end  of  a  beam  which  brings  a  longitudinal  load  of  60,000  pounds 
and  a  bending  moment  of  180,000  in.-lb.  upon  the  column.  The 
column  is  reinforced  with  four  1-inch  square  steel  bars  at  the  corners, 
the  centers  of  steel  being  2  inches  from  surf  apes  of  concrete.  n=15. 
Find  the  unit  stresses  on  the  concrete. 


FIG.  59. — Column  with  Eccentric  Load. 


Solution. — 

Ic=  12X16X16X16/12=4096. 
60000  180000X8 


'      192+14X4  '  4096+14X144 
/'c=242-235  =  71b/in.2 


JS=4X12X12/4  =  144. 
=  242+235=477  lb./in.2, 


Complete  discussions  of  the  principles  of  reinforced  concrete 
design  with  applications  to  structures  is  given  in  "  Concrete,  Plain 
and  Reinforced,"  by  Taylor  and  Thompson,  and  in  "  Principles  of 
Reinforced  Concrete  Construction/'  by  Turneaure  and  Maurer. 


CHAPTER  VII 
RETAINING  WALLS 

ART.  33.    PRESSURE  OF  EARTH  AGAINST  A  WALL. 

123.  Theories  of  Earth  Pressure. — The  lateral  pressure  of  a  mass 
of  earth  against  a  retaining  wall  is  affected  by  so  many  variable 
conditions  that  the  determination  of  its  actual  value  in  a  particular 
instance  is  practically  impossible. 

Several  theories,  based  in  each  case  upon  certain  ideal  conditions, 
have  been  proposed,  none  of  which  are  more  than  very  rough  approxi- 
mations to  the  conditions  existing  in  such  structures.  These  theo- 


FIG.  60. — Pressure  of  Earth  against  a  Wall. 

ries  assume  that  the  earth  is  composed  of  a  mass  of  particles  exerting 
friction  upon  each  other  but  without  cohesion,  or  that  the  pressure 
against  the  wall  is  caused  by  a  wedge  of  earth  which  tends  to  slide 
upon  a  plane  surface  of  rupture,  as  shown  in  Fig.  60.  Formulas  for 
the  resultant  thrust  against  the  wall  have  been  produced  in  accord- 
ance with  the  various  theories  by  several  methods,  they  differ  mainly 
in  the  direction  given  to  the  thrust  upon  the  wall. 

Coulomb's  Theory. — A  formula  for  computing  the  lateral  thrust 
against  a  wall  was  proposed  by  Coulomb  in  1773.  Coulomb  assumed 
that  the  thrust  was  caused  by  a  prism  of  earth  (BAC,  Fig.  60)  sliding 

214 


PRESSURE  OF  EARTH  AGAINST  A  WALL       215 

upon  any  plane  AC  which  produces  the  maximum  thrust  upon  the 
wall.  There  is  a  certain  slope  (AD,  Fig.  60)  at  which  the  material  if 
loosely  placed  will  stand.  This  is  known  as  the  natural  slope,  and 
the  angle  made  by  this  slope  with  the  horizontal  as  the  angle  of  fric- 
tion of  the  earth.  On  slopes  steeper  than  the  natural  slope,  there  is  a 
tendency  for  the  earth  to  slide  down,  and  if  held  by  a  wall,  pressures 
are  produced  which  depend  upon  the  frictional  resistance  to  sliding. 
The  thrust  is  assumed  by  Coulomb  to  be  normal  to  the  wall,  and 
the  pressure  upon  the  plane  of  rupture  to  be  inclined  at  the  angle  of 
friction  to  the  normal  to  the  plane. 

Let  h  =  height  of  wall; 

P  =  resultant  pressure  upon  a  unit  length  of  wall; 

R  =  pressure  upon  the  plane  of  rupture; 

G  =  weight  of  the  wedge  of  earth ; 

e  =  weight  of  earth  per  cubic  foot; 

0  =  angle  of  friction  of  earth; 

a  =  angle  between  the  back  of  wall  and  plane  of  rupture. 

If  the  back  of  the  wall  be  vertical  and  the  surface  of  earth  horizon- 
tal, from  Fig.  60, 

tan  a 
tan  (a-\-<t>Y 

For  maximum  value  of  P,  a  =  45°  —  ^,  and  the  plane  of  rupture 

bisects  the  angle  between  the  back  of  the  wall  and  the  natural  slope. 
Substituting  this  value, 


P  varies  as  the  square  of  h,  and  is  therefore  applied  at  a  distance 
h/3  above  the  base  of  the  wall.  This  is  the  same  in  all  of  the  theories. 

Poncelet's  Theory. — In  1840  Poncelet  proposed  to  modify  the 
method  of  Coulomb  by  making  the  thrust  upon  the  wall  act  at  the 
angle  of  friction  with  the  normal  to  the  wall. 

Before  the  wall  can  be  overturned  about  its  toe  (F,  Fig.  61)  the 
back  of  the  wall  (A  B)  must  be  raised  and  slide  upon  the  earth  behind 
it,  thus  calling  into  play  the  friction  of  the  earth  upon  the  wall  as  a 
resistance.  As  the  friction  of  earth  upon  a  rough  masonry  wall  is 
greater  than  that  of  earth  upon  earth,  a  nlm  of  earth  would  be  carried 
with  the  wall  and  slide  upon  the  earth  behind  and  the  angle  of  friction 
is  usually  taken  as  equal  to  the  natural  slope  of  the  earth. 


216 


RETAINING  WALLS 


Let   6  =  the  angle  made  by  the  back  of  the  wall  with  the  horizontal  ; 
z  =  the  angle  made  by  the  earth  surface  with  the  horizontal. 

Following  the  same  procedure  as  in  developing  Coulomb's  formula, 
we  find  the  pressure  against  the  wall, 

P  =  i^2 Si»2  («-*) 

sin  (4>—i),  sin  2</> 


FIG.  61.  —  Poncelet's  Theory  of  Pressure. 
For  a  vertical  wall  and  horizontal  earth  surface 

o°), 

eh2  cos  0 


=  90°  and 


which  is  the  formula  proposed  by  Poncelet. 

Rankine's  Theory.  —  Rankine  considered  the  earth  to  be  made  up 
of  a  homogeneous  mass  of  particles,  possessing  frictional  resistance 
to  sliding  over  each  other  but  without  cohesion.  He  deduced  for- 
mulas for  the  pressure  upon  ideal  plane  sections  through  an  unlimited 
mass  of  earth  with  plane  upper  surface,  the  earth  being  subject  to  no 
external  force  except  its  own  weight,  and  determined  the  direction 
of  the  pressure  from  these  assumptions. 

Rankine  found  that  the  resultant  pressure  upon  any  vertical 
plane  section  through  a  bank  of  earth  with  plane  upper  surface  is 
parallel  to  the  slope  of  the  upper  surface  (see  Fig.  62)  . 

Let    E  =  the  pressure  upon  the  vertical  section; 

^  =  the  angle  made  by  the  inclination  of  the  upper  surface 
with  the  horizontal; 


Then 


PRESSURE  OF  EARTH  AGAINST  A  WALL 

0  =  the  angle  of  friction  of  the  earth; 
e  =  the  weight  per  cubic  foot  of  the  earth; 
$=the  height  of  vertical  section  through  earth. 


217 


,    eS2        .  cos  ^  —  Vcos2  i— cos2  0 
=— cosz--  .  , 

«  cos  i + V  cos2  i — cos2  </> 


is  Rankine's  formula  for  earth  pressure.  This  pressure  acts  upon 
the  vertical  section  at  a  distance  S/3  from  its  base,  and  makes  an 
angle  i  with  the  horizontal. 

Rankine's  formula  may  be  produced  in  the  same  manner  as 
Poncelet's  by  assuming  the  pressure  parallel  to  the  upper  slope. 


FIG.  62. — Pressure  of  Earth 

Thus  in  Fig.  61  if  the  angle  made  by  P  with  the  normal  to  the  wall 
be  equal  to  it  we  find 

eS2  cos2  0 


sin  (0  — a)  sin(0-j-fr')\2' 
cos2  i  ) 


which  may  be  transformed  1  into  Rankine's  formula  as  given  above. 

Weyrauchs  theory  is  practically  the  same  as  Rankine's  although 
produced  in  a  different  way. 

Cohesion. — In  all  of  the  ordinary  formulas  for  earth  pressure,  the 
effect  of  cohesion  is  neglected.  Experiments  indicate  that  this  effect  is 
not  sufficient  to  affect  very  materially  the  actual  pressure  upon  a  wall. 
It  causes  the  earth  to  break  off  and  slide  upon  a  concave  surface  in- 
stead of  a  plane  surface.  At  the  upper  surface  of  the  earth,  the  cohe- 
1  Wm.  Cain,  Practical  Designing  of  Retaining  Walls,  1914,  p.  103. 


218  RETAINING  WALLS 

sion  is  sufficient  to  overcome  the  lateral  thrust  and  cause  the  earth 
to  stand  in  a  vertical  position,  while  as  the  lateral  thrust  increases 
with  the  depth,  the  cohesion  becomes  relatively  less  important  and 
the  surface  of  rupture  flattens  out.  When  earth  is  placed  behind  a 
wall  after  it  is  constructed  cohesion  is  probably  negligible  at  first, 
although  after  the  earth  has  become  compacted  may  develop  in  some 
cases  so  that  practically  no  pressure  comes  against  the  wall.  It  is 
so  uncertain  that  no  reliance  should  be  placed  upon  it  in  designing 
walls. 

Value  of  Theories.  —  On  account  of  the  variable  nature  of  the 
material,  it  is  evident  that  estimates  of  earth  pressures  are  only 
rough  approximations  to  the  actual  pressures.  The  material  assumed 
as  possessing  uniform  friction  and  without  cohesion  does  not  exist  in 
practice.  The  general  laws  developed,  however,  do  give  rational 
methods  of  reaching  reasonable  estimates  upon  which  safe  designs 
may  be  based. 

Experiments  upon  sand  pressures,  and  experience  with  walls  in 
use,  indicate  that  Coulomb's  use  of  horizontal  earth  pressures,  or 
Rankine's  thrust  parallel  to  earth  surface,  where  the  surface  is  near  the 
horizontal,  give  thrusts  much  greater  than  those  actually  produced 
upon  walls  with  vertical  backs.  For  such  walls,  the  use  of  the 
Poncelet's  formulas,  taking  into  account  the  friction  of  the  earth 
on  the  back  of  the  wall,  give  results  which  seem  to  agree  fairly  well 
with  experiment  and  experience. 

For  walls  leaning  forward,  so  that  considerable  weights  of  earth 
rest  upon  them,  Rankine's  formulas  may  be  applied  to  find  the 
thrust  upon  the  vertical  section  through  the  earth  at  the  inner  edge 
of  the  base  of  the  wall.  This  thrust,  combined  with  the  weight  of 
earth  resting  upon  the  wall,  gives  the  thrust  against  the  wall. 

124.  Computation  of  Earth  Thrusts.  —  When  the  back  of  a  wall  is 
nearly  vertical,  the  thrust  may  usually  be  taken  as  making  the  angle 
of  friction  with  a  normal  to  the  surface  of  the  wall,  as  assumed  in  the 
theory  of  Poncelet.  For  such  walls  the  thrust  may  be  obtained  from 
the  formula  already  given: 

eh?  sin2  (0-0) 

M 

•  2  n    •   //.  ,  ,\7  ,  -;)-  sin  20    \ 

sin2  0-sm(0+0)u-f 
' 


/    sin  (0-;)-  s 
A/-  —  ,„     ..     . 
\sm  (B—i)   sm 


eh2 
If  we  place  P=—Q,  values  of  Q  may  be  tabulated  for  various 

2i 

slopes  and  angles  of  friction  as  shown  in  Table  XVII.     The  values  of 
P  obtained  by  this  method  are  supposed  to  act  against  the  wall  at  a 


PRESSURE  OF  EARTH  AGAINST  A  WALL 


219 


distance  h/3  above  the  base,  and  make  the  angle  of  friction  with  the 
normal  to  the  wall. 

TABLE  XVIL— EARTH  PRESSURE  AGAINST  A  WALL 

Values  of  Q  in  Formula  (1),  P=^r--Q 


Batter  of  Back 
of  Wall. 

SLOPE  OF  UPPER 
SURFACE  OF  EARTH. 

ANGLE  OF  FRICTION,  <f>. 

Angle  i. 

Vertical 
to  Hori- 
zontal. 

20° 

25° 

30° 

35° 

40° 

45° 

33°  40' 

l  to  H 

.59 

.39 

.28 

29°  45' 

1  to  If 

.76 

.45 

.34 

.25 

Vertical        } 

26°  30' 
21°  50' 

Ito2 

.54 
.46 

.39 
.35 

.32 
.30 

.23 
.22 

.61 

0  =  90° 

18°  30' 

1  to  3 

.72 

.52 

.40 

.33 

.28 

.21 

14°  00' 

1  to  4 

.58 

.45 

.36 

.30 

.25 

.19 

0°00' 

Level 

.43 

.37 

.30 

.26 

.21 

.18 

33°  40' 

to  H 

.72 

.50 

.37 

29°  40' 

to  If 

.90 

.56 

.44 

.35 

26°  30' 

v\s   J.  4 

to  2 

.64 

.49 

.40 

.32 

1  in  10 
0  =  95°  40' 

21°  50' 

18°  30' 

to  3 

.70 
.60 

.56 

.48 

.44 
.40 

.36 
.34 

.30 

.28 

.82 

14°  00' 

to  4 

.66 

.52 

.40 

.35 

.31 

.25 

0°00' 

Level 

.48 

.40 

.34 

.30 

.26 

.22 

33°  40' 

1  to  H 

.91 

.62 

.49 

29°  45' 

Itolf 

1.08 

.68 

.55 

.46 

26°  30' 

1  to  2 

77 

.60 

.50 

.42 

1  in  5 
0  =  101°  20' 

21°  50' 

18°  30' 

1  to  2^ 
1  to  3 

.93 

.80 
.68 

.66 
.57 

.54 

.48 

.45 
.42 

.38 
.36 

14°  00' 

1  to  4 

.75 

.60 

.48 

.41 

.38 

.32 

I 

0°00' 

Level 

.52 

.46 

.40 

.34 

.30 

.27 

When  a  mass  of  earth  rests  upon  a  wall,  as  in  a  wall  with  sloping 
back  or  a  reinforced  concrete  wall,  the  formula  of  Rankine  for  pres- 
sure upon  a  vertical  section  may  be  applied.  This  pressure  combined 
with  the  weight  of  the  earth  resting  upon  the  wall  gives  the  thrust 
against  the  wall. 

The  value  of  the  pressure  upon  the  vertical  section  is  given  by 
Rankine's  formula: 


eS2         .  cos  i  —  Vcos2  i — cos2  <£  _  eS2  „ 
2  cos  i + Vcos2  i — cos2  0      2 


(2) 


220 


RETAINING  WALLS 


Values  of  K  corresponding  to  various  values  of  i  and  $  are  tabu- 
lated in  Table  XVIII,  thus  greatly  reducing  the  labor  of  computing 
the  pressures.  E  as  computed  from  this  formula  is  supposed  to  act 
at  a  distance  S/3  from  the  bottom  of  the  section  and  to  be  parallel 
to  the  upper  surface  of  the  earth.  S  in  this  formula  is  the  height 
of  the  earth  section  and  not  the  height  of  the  wall. 

TABLE  XVIII —PRESSURES  UPON  VERTICAL  SECTIONS  THROUGH 

EARTH 

Values  of  K  in  Formula  (2)  -E=K 


SLOPE  OF  UPPER 
SURFACE  OF  EARTH. 

ANGLE  OF  FRICTION. 

Angle  i. 

Vertical  to 
Horizontal. 

20° 

25° 

30° 

35° 

40° 

45° 

33°  40' 
29°  45' 
26°  30' 
21°  50' 
18°  30' 
14°  00' 
0°00' 

ItoU 
1  to  If 
1  to  2 
Ito2i 
Ito3 
1  to  4 
Level 

0.59 
0.45 
0.39 
0.34 
0.31 
0.29 
0.27 

0.36 
0.32 
0.29 
0.27 
0.24 
0.23 
0.22 

0.26 
0.23 
0.21 
0.20 
0.19 
0.18 
0.18 

0.76 
0.54 
0.45 
0.40 
0.36 
0.33 

0.60 
0.52 
0.45 
0.40 

0.72 
0.59 
0.50 

Angle  of  Friction. — In  order  to  be  able  to  apply  any  of  the  formulas 
for  determining  earth  pressures,  it  is  necessary  to  know  the  weight  per 
unit  volume  and  the  angle  of  friction  of  the  earth.  These  vary  with 
the  kind  of  material  to  be  filled  behind  the  wall  and  its  condition  as 
to  compactness  and  moisture. 

The  natural  slope  for  the  earth  is  the  slope  at  which  the  surface 
of  the  material  will  stand  when  dumped  into  piles,  the  frictional 
resistance  keeping  the  surface  layer  from  sliding  or  rolling  down  the 
slope.  The  angle  of  sliding  friction  of  a  wedge  of  earth  upon  an 
earth  surface  may  not  be  the  same  as  the  inclination  of  the  natural 
slope.  Values  of  sliding  friction  as  determined  by  experiment  vary 
considerably  for  the  same  material,  and  it  is  possible  that  much  of  the 
variation  is  due  to  the  methods  of  testing  rathei  than  to  differences 
in  the  materials.  The  natural  slope  of  a  particular  material  may 
usually  be  approximately  determined  without  difficulty  and  its  use 
instead  of  the  angle  of  sliding  friction  would  ordinarily  be  safe.  Table 
XIX  gives  approximate  values  of  the  angle  of  internal  friction,  the 
natural  slopes  and  weights  of  various  materials  commonly  met  in 
construction. 


PRESSURE  OF  EARTH  AGAINST  A  WALL 


221 


TABLE  XIX.— FRICTION  ANGLES  AND  WEIGHTS  OF  MATERIALS 


Kind  of  Material. 

Angle  of 
Friction. 

Natural  Slope, 
Horizontal  to 
Vertical. 

Weight  per 
Cubic  Foot. 

Clav,  dry 

35° 

1  5  to  1 

110 

Clay,  damp  

40° 

1.2  to  1 

110 

Clay,  wet        

20° 

3  0  to  1 

120 

Sand  dry 

35° 

1  5  to  1 

100 

Sand,  moist  

40° 

1  .  3  to  1 

100 

Sand,  wet 

25° 

2  0  to  1 

115 

Gravel  and  sand  

40° 

1.5  to  1 

110 

Broken  rock  .... 

45° 

1  .  2  to  1 

110 

Surcharged  Walls.  —  The  formulas  for  earth  pressure  already  given 
assume  the  earth  to  carry  only  its  own  weight  and  the  upper  surface 
to  slope  from  the  top  of  the  wall.  When  the  earth  behind  the  wall 
carries  a  load  upon  its  surface,  as  when  supporting  a  railway  track 
or  a  pile  of  material  of  any  sort,  the  pressure  against  the  wall  is 
increased  uniformly  over  its  entire  depth. 

If  w  is  the  weight  of  the  load  per  unit  area  of  earth  surface, 
Formula  (1)  becomes, 

.......     (3) 


The  point  of  application  of  P  is  at  a  distance 

l_  eh+Zw 

3'eh+2w  ' 
above  the  base  of  the  wall. 

In  the  same  manner  for  the  pressure  on  a  vertical  section  through 
the  mass  of  earth,  Formula  (2)  becomes 


E=l^- 


(4) 


and  its  point  of  application  is  at  a  distance 

I   eS+3w 


3  eS+2w 


S. 


125.  Graphical  Method. — When  the  surface  of  earth  is  irregular 
or  broken,  the  formulas  do  not  apply,  although  it  is  usually  possible 
to  approximate  the  plane  surfaces  with  sufficient  accuracy.  Graph- 
ical determination  of  earth  pressures  may  be  made  when  the  slope  of 
the  surface  is  not  too  great.  When  the  surface  slope  is  near  the 
natural  slope  for  the  material,  these  methods  cannot  be  used. 


222 


RETAINING  WALLS 


A  graphical  method  is  shown  in  Fig.  63.  OA  is  the  back  of  a  wall, 
and  A  BCD,  etc.,  the  upper  surface  of  the  earth  resting  against  it. 
Divide  the  earth  into  a  number  of  prisms  by  the  lines  OB,  OC,  etc. 
On  the  line  oa  lay  off  on  some  convenient  scale  ab,  be,  etc.,  equal 
respectively  to  the  weights  of  the  prisms  OAB,  OBC,  OCD,  etc. 

From  a  draw  the  lines  061,  aci,  etc.,  making  the  angle  of  friction 
(</>)  with  the  normals  to  OB,  OC,  OD,  etc.,  respectively.  From  the 
points  b,  c,  d,  etc.,  draw  the  lines  661,  cci,  ddi,  etc.,  making  the 
angle  of  friction  (<j>)  with  the  back  of  the  wall  (OA),  to  intersection 
with  the  lines  abi,  aci,  etc.,  respectively.  The  lengths  bbi,cci,  ddi,  etc., 
will  then  represent,  on  the  scale  to  which  the  weights  were  laid  off, 
the  thrusts  of  the  prisms  between  the  back  of  the  wall  and  the  planes 
OB,  OC,  etc.,  respectively. 


B 


FIG.  63. — Graphical  Determination  of  Earth  Pressures. 

In  the  figure,  ee\  is  the  maximum  thrust,  caused  by  the  prism  between 
OA  and  OE,  showing  OE  to  be  the  plane  of  rupture.  This  resultant 
thrust  will  act  at  a  distance  h/3  from  the  base  of  the  wall,  at  the  angle 
of  friction  with  the  normal  to  the  wall. 

Detailed  discussions  of  methods  of  determining  earth  pressures 
are  given  in  "Retaining  Walls  for  Earth"  by  M.  A.  Howe,  New  York, 
1896,  and  in  "Practical  Designing  of  Retaining  Walls,"  by  Wm.  Cain, 
New  York,  1914.  An  interesting  paper  by  E.  P.  Goodrich  in  Trans- 


SOLID   MASONRY  WALLS 


223 


actions,  American  Society  of  Civil  Engineers,  December,  1904,  gives 
results  of  experiments  for  determination  of  internal  friction  and 
lateral  pressure  of  earth. 


ART.   34.     SOLID   MASONRY  WALLS 

126.  Stability  of  Walls. — A  masonry  retaining  wall  may  fail  in 
either  of  three  ways: 

1.  By  overturning  or  rotating  about  its  toe. 

2.  By  crushing  the  masonry. 

3.  By  sliding  on  a  horizontal  joint. 

Insufficient  foundation  is  probably  the  most  common  cause  of 
failure  of  retaining  walls.  This  is  not,  however,  due  to  failure  of  the 
wall  itself,  but  to  lack  of  sufficient  footing  or  other  support  when 
placed  upon  compressible  or  soft  soils  or  to  lack  of  proper  drainage. 
This  is  discussed  in  Art.  36. 


FIG.  64. — Stresses  upon  Retaining  Walls. 

In  Fig.  64,  A  BCD  is  a  wall  with  vertical  face  supporting  a  bank  of 
earth  as  shown. 

Let   P  =  thrust  of  earth  against  the  wall; 

V  =  Vertical  component  of  P; 

H  =  horizontal  component  of  P; 

W  =  weight  of  wall  acting  through  its  center  of  gravity; 

R  =  resultant  pressure  on  base  A  B ; 


224  RETAINING  WALLS 

6  =  width  of  base  of  wall; 
a=  width  of  top  of  wall; 

d  =  distance  from  face  of  wall  to  its  center  of  gravity; 
/c  =  unit  compression  on  masonry  at  toe  of  wall; 
x  =  distance  from  toe  of  wall  to  point  of  application  of 

resultant  pressure  upon  the  base; 
0  =  angle  made  by  R  with  base  of  wall. 

Resisting  Moment.  —  The  moment  of  the  thrust  about  the  toe 
of  the  wall  at  B  is  M  =  HX-  VX  (26+a) 


. 

o 

This  moment  tends  to  overturn  the  wall  by  causing  rotation 
about  B,  and  is  resisted  by  the  moment  of  the  weight  of  wall  in  the 
opposite  direction.  This  moment  is  Mw  =  Wd. 

When  these  moments  are  equal  (MW—MP  =  Q),  the  resultant  R 
obtained  by  combining  P  and  W  passes  through  B  and  the  wall  is 
on  the  point  of  overturning.  The  ratio  MW/MP  is  the  factor  of 
safety  against  overturning. 

When  Mw  is  greater  than  MPJ  R  will  cut  the  base  of  the  wall  to 
the  right  of  B.  Placing  MT—MW—MP  we  have 


t 

6  ,  6 

from  which  we  find  the  distance  of  the  point  of  application  of  R 
from  B: 

_3Wd+V(2b+a)-Hh 

3(W+V) 

This  point  of  application  of  R  may  also  be  found  graphically  as 
shown  in  Fig.  63. 

The  resultant  R  should  always  cut  the  base  of  the  wall  within 
its  middle  third  (x>6/3)  in  order  that  the  pressure  may  be  distrib- 
uted over  the  whole  section  of  the  base  and  there  may  be  no  tend- 
ency for  the  joint  to  open,  or  no  tensile  stress  developed  at  the  inner 
edge  (A)  of  the  section. 

Crushing  of  Masonry.  —  The  unit  stress  at  the  toe  of  the  wall  (B) 
must  not  exceed  the  safe  crushing  strength  of  the  masonry.  The 
distribution  of  stress  over  the  section  depends  upon  the  position  of 
the  point  of  application  of  the  resultant  (R).  When  x  =  b/3,  the 


stress  at  A  will  be  zero,  and  the  stress  at  B,  fc  =  --  =-  --  -.     If  x  be 
less  than  6/3,  the  pressure  will  be  distributed  over  a  distance  3x 


SOLID   MASONRY  WALLS  225 

2(W  -4-V) 
from  the  toe  (B),  and  the  maximum  stress,  fe  =  —  —  «  -  •    When 

oX 

x  is  greater  than  6/3  the  maximum  compression, 

(TT+7)(46-6x) 

Jc=  ^2  «  .......        (6) 

Resistance  to  Sliding  depends  upon  the  development  of  sufficient 
friction  in  any  joint  through  the  wall  to  overcome  the  pressure 
parallel  to  the  joint.  Thus  (Fig.  64)  in  order  that  no  sliding  occur 
at  the  base  of  the  wall,  the  frictional  resistance  in  the  joint  A  B  must  be 
greater  .than  the  horizontal  component  of  the  thrust  R.  This  will 
be  the  case  when  R  makes  an  angle  (|3)  with  the  normal  to  AB 
that  is  less  than  the  angle  of  friction  of  masonry  sliding  upon  masonry. 

TT 

Tan  fi  =       ,)  must  be  less  than  the  coefficient  of  friction  of  the 


masonry. 

In  the  construction  of  heavy  walls,  resistance  to  sliding  may  be 
increased  by  breaking  joints  so  that  no  continuous  joint  exists  through 
the  wall.  Joints  inclined  from  the  front  to  the  back  of  the  wall  are 
also  sometimes  used  so  as  to  bring  the  resultant  pressure  more  nearly 
normal  to  the  joint. 

127.  Empirical  Design.  —  In  the  practical  designing  of  retaining 
walls,  engineers  have  commonly  used  empirical  rules  given  by  certain 
prominent  authorities,  or  have  assumed  dimensions  based  upon  their 
own  experiences.  The  uncertain  and  conflicting  nature  of  the 
assumptions  used  in  producing  the  formulas  based  upon  the  various 
theories,  and  the  lack  of  satisfactory  experimental  data  has  caused 
the  use  of  dimensions  shown  by  experience  to  be  safe  and  in  very 
many  instances  probably  quite  excessive. 

Trautwine's  rules  have  been  extensively  used  for  many  years, 
and  are  as  follows  J  for  vertical  walls  : 

When  the  backing  is  deposited  loosely,  as  usual,  as  when  dumped  from  carts, 
cars,  etc., 
Wall  of  cut  stone,  or  first-class  large  ranged  rub- 

ble, in  mortar  ............................  35  of  its  entire  vertical  height 

Wall  of  good  common  scabbled  mortar-rubble, 

or  brick  ............  .....................  4    of  its  entire  vertical  height 

Wall  of  well-scabbled  dry  rubble  ...............  5    of  its  entire  vertical  height 

With  good  masonry,  however,  we  may  take  the  height  from  the 
ground  surface1  up,  instead  of  the  total  height  as  above  indicated. 
When  the  wall  has  a  sloping  or  offset  back,  the  thickness  above 
1  Trautwine's  Engineer's  Pocket-Book. 


226  RETAINING  WALLS 

given  may  be  used  as  the  mean  thickness,  or  thickness  at  the  mid- 
height. 

Baker's  Rules. — Sir  Benjamin  Baker,  from  an  extended  experience 
in  the  construction  of  walls  under  many  differing  conditions,  and 
after  numerous  experiments  upon  the  thrust  of  earth,  gives1  the 
following  statement  of  his  views  upon  the  design  of  retaining  walls: 

Experience  has  shown  that  a  wall  one-quarter  of  the  height  in  thickness,  and 
battering  1  inch  or  2  inches  per  foot  on  the  face,  possesses  sufficient  stability 
when  the  backing  and  foundation  are  both  favorable.  The  Author,  however, 
would  not  seek  to  justify  this  proportion  by  assuming  the  slope  of  repose  to  be 
about  1  to  1,  when  it  is  perhaps  more  nearly  1£  to  1,  and  a  factor  of  safety  to  be 
unnecessary,  but  would  rather  say  that  experiment  has  shown  the  actual  lateral 
thrust  of  good  filling  to  be  equivalent  to  that  of  a  fluid  weighing  about  10  pounds 
per  cubic  foot,  and  allowing  for  variations  in  the  ground,  vibrations,  and  con- 
tingencies, a  factor  of  safety  of  2,  the  wall  should  be  able  to  sustain  at  least  20 
pounds  fluid  pressure,  which  will  be  the  case  if  one-quarter  of  the  height  in 
thickness. 

It  has  been  similarly  proved  by  experience  that  under  no  ordinary  conditions 
of  surcharge  or  heavy  backing  is  it  necessary  to  make  a  retaining  wall  on  a  solid 
foundation  more  than  double  the  above,  or  one-half  of  the  height  in  thickness. 
Within  these  limits  the  engineer  must  vary  the  strength  in  accordance  with 
the  conditions  affecting  the  particular  case. 

The  rules  of  Sir  Benjamin  Baker  give  walls  considerably  lighter 
than  those  of  Trautwine,  and  the  tendency  in  recent  practice  has  been 
to  somewhat  reduce  the  thicknesses  for  walls  backed  with  good 
materials  and  built  under  favorable  conditions.  Where  from  lack  of 
drainage  or  other  cause,  the  backing  is  liable  to  get  into  soft  condition, 
it  may  be  necessary  to  considerably  increase  thickness. 

128.  Using  Formulas  in  Design. — The  design  of  a  wall  to  sustain 
a  bank  of  earth  is  a  comparatively  simple  matter  once  the  earth 
pressure  has  been  determined.  The  difficulties  met  are  those  of 
judging  the  character  of  the  material  and  its  probable  pressure 
against  the  wall.  It  is  probable  that  in  most  instances  the  full 
pressures  that  theoretically  might  come  upon  the  wall  are  not  actually 
developed.  The  design  should  be  made  for  the  worst  conditions 
which  may  reasonably  be  expected  to  occur,  but  the  construction 
of  heavy  walls  to  provide  for  bad  conditions  which  are  not  likely  to 
occur,  and  which  may  be  met  by  proper  attention  to  drainage  and 
proper  care  in  placing  the  backing,  is  unnecessarily  expensive  and 
wasteful. 

For  walls  with  vertical  or  nearly  vertical  backs, .  Poncelet's  for- 
mulas, taking  into  account  the  friction  of  the  earth  on  the  back  of 

1  The  Actual  Lateral  Pressure  of  Earth,  Van  Nostrand  Science  Series,  and 
Proceedings,  Institution  of  Civil  Engineers,  Vol.  LXV,  p.  183. 


SOLID   MASONRY  WALLS  227 

the  wall,  give  thicknesses  for  walls  which  agree  fairly  well  with  the 
results  of  experience  and  not  differing  greatly  from  the  rules  sug- 
gested by  Sir  Benjamin  Baker. 

in  designing  by  this  method,  the  pressure  of  earth  is  obtained  by 
the  use  of  Formula  (1),  or  from  Table  XVII,  a  section  of  wall  is 
assumed  and  its  sufficiency  investigated. 

Example  1. — A  masonry  wall,  22  feet  high,  is  to  support  a  bank 
of  earth  whose  surface  has  an  upward  slope  of  1  to  3  from  the  top 
of  the  wall.  The  backing  is  ordinary  earth  whose  friction  angle 
may  be  taken  at  35°.  Weight  of  masonry  is  150  pounds  and  of  earth 
100  pounds  per  cubic  foot.  Find  proper  section  for  the  wall. 

Solution. — Try  a  rectangular  wall  with  thickness  of  7.5  f  et. 
From  Table  XVII,  we  find  Q  =  .33.  Then 

D    eh2n     100X22X22X.33 

P  =  -p-Q  =  -         -7:—         - = 7986  pounds  per  foot  of  length  of  wall. 

A  -• 

As  P  makes  angle  of  35°  with  normal  to  back  of  wall, 

H  =  Pcos  35°  =  6770  pounds  and  V  =  P  sin  35°  =  4580  pounds. 
W  =  22  X  7 . 5  X 150  =  24,750  pounds. 

From  (5),  we  find 

3X24750X3.75+4580X3X7.5-6770X22 


3(24750+4580) 


=  2.64 


and  the  resultant  (R)  comes  just  within  the  middle  third  of  the  base. 
The  crushing  stress  on  the  masonry  at  the  toe  of  the  wall  is  (6) 

_  (W+  V)  (46  -  6or)  _  (24750+4580)  (4  X  7.5  -  6  X  2.64) 
fc~          ~W~  ~  7.5X7.5  lb'/tt* 

which  would  be  quite  safe  for  any  ordinary  masonry. 

tan  0  =  T^Ty  =  24750"- 4580  =  <231>  °r  ®  =  13°' 

and  sliding  could  not  occur. 

Battered  Face. — The  face  of  the  wall  may  be  battered,  so  as  to 
diminish  the  width  at  top  by  one- third,  using  the  same  width  of  base 
without  decreasing  its  stability. 

Battered  Back. — A  wall  with  battered  back  may  be  used.  Assume 
a  top  thickness,  a  =  5.5,  and  base  thickness,  6  =  9.5.  The  angle 
made  by  the  back  of  the  wall  with  the  horizontal  6  =  100°  20'.  From 

„     eh2Q     100  X  22  X 22 X47 
Table    XVII,    we    find    Q  =  .47,    then    P  =  —e^  =  — 


228  RETAINING  WALLS 

=  1  1624  pounds.    H  =  P  cos  (0+<j>  -  90)  =  8170  pounds,  and  V  =  P  sin 
((9+0  -  90°)  =  8270  pounds.   W  =  5'5+9'5  X  22  X  150  =  24750  pounds. 

SB 

From  (3), 

_3X24750X3.  83+8270(2X9.  5+5.  5)  -8170X22_Q 

3(24750+8270) 

R  cuts  the  base  practically  at  one-third  its  width  from  the  toe. 

2(W-\-V) 
The  crushing  stress  at  the  toe  is  fc=  --  =-  --  =  6950  pounds, 

a  little  less  than  for  the  rectangular  wall. 

tan  ft  =  o^yKfl  i  0070  =  -247,    within    safe   limits  but    somewhat 

more  than  for  the  rectangular  wall. 

Example  2.  —  A  retaining  wall  20  feet  high  is  to  support  a  hori- 
zontal bank  of  eaHh  carrying  a  railway  track.  If  the  maximum 
train  load  is  taken  at  800  pounds  per  square  foot  of  surface,  and  the 
angle  of  friction  of  the  earth  at  30°,  find  the  thickness  of  wall  required 
by  Poncelet's  formula,  w  =  150  pounds  and  e  =  100  pounds  per 
cubic  foot. 

Solution.  —  Assume  a  thickness  of  wall  of  9  feet.  From  Table 
XVII,  we  have  Q  =  30.  Then  (3) 


3Q= 

H  =  P  cos  0  =  10800  X  .866  =  93 
and 


H  =  P  cos  0  =  10800  X  .866  =  9350  pounds, 

V  =  10800  X  .5  =  5400  pounds. 
JF  =  9  X  20  X  150  =  27000  pounds. 


Using  (5), 

_3X27000X4.5+5400X9X3-9350X20_Q 
3(27000+5400) 

The  resultant  thrust  cuts  the  base  within  the  middle  third,  and  a 
little  less  width  might  answer. 

The  crushing  stress  at  the  toe  of  the  wall  is 

pounds.       ..,.-:" 


C 

The  minimum  thickness  allowable  for  a  solid  wall  is  that  which 
causes  the  resultant  thrust  (R)  to  cut  the  base  at  a  distance  x  =  l/3 
from  the  toe  of  the  wall.  For  a  rectangular  wall,  the  width  bears  a 
direct  ratio  to  the  height  for  any  particular  values  for  weights  of 


REINFORCED   CONCRETE  WALLS 


229 


materials  and  angles  of  friction.  Table  XX  gives  minimum  values 
of  thickness  ratio,  by  Poncelet's  formula  for  walls  in  which  the 
weight  of  masonry  is  taken  as  150  lb./ft.3  and  the  weight  of  earth 
as  100  lb./ft.3 

TABLE  XX.— MINIMUM    THICKNESS   OF   WALLS   BY   PONCELET'S 

FORMULA 

Values  of  b/h,  when  w  =  150  lb./ft.3  and  e  =  100  lb./ft.3 


Slopes  of  Earth  Sur- 
face Vertical  to 
Horizontal. 

ANGLES  OF  FRICTION. 

20° 

25° 

30° 

35° 

40° 

45° 

Ito  l\ 

0.39 

0.31 

0.25 

ltol| 

.... 

.... 

0.46 

0.35 

0.29 

0.24 

Ito2 

0.41 

0.34 

0.28 

0.23 

Ito2i 

.... 

0.46 

0.39 

0.33 

0.27 

0.23 

Ito  3 

0.53 

0.43 

0.37 

0.32 

0.27 

0.23 

Ito  4 

0.49 

0.41 

0.35 

0.30 

0.26 

0.22 

Level 

0.43 

0.38 

0.33 

0.29 

0.25 

0.22 

For  walls  battered  or  stepped  on  the  back  the  minimum  thickness 
given  in  the  table  may  be  used  as  the  average  thickness  at  the  middle 
of  the  height.  This  gives  a  broader  base  to  the  wall  and  gives  a 
larger  factor  of  safety  against  overturning,  but  requires  the  same 
volume  of  masonry  to  keep  the  resultant  thrust  within  the  middle 
third  of  the  base. 

Walls  computed  as  rectangular  may  be  battered  on  the  face  to  an 
extent  which  lessens  the  top  thickness  by  one-third  without  increas- 
ing the  base  thickness.  This  slightly  decreases  the  resisting  moment, 
but  increases  the  value  of  x,  lessens  the  pressure  at  the  toe,  and  does 
not  impair  the  stability  of  the  wall. 


ART.   35.     REINFORCED    CONCRETE  WALLS 

129.  Types  of  Reinforced  Concrete  Retaining  Walls.— There  are 
two  types  of  reinforced  concrete  retaining  walls  in  common  use : 

1.  The  cantilever  type  and  2,  the  counterforted  type. 

Both  of  these  depend  upon  the  weight  of  earth  carried  by  the  base 
of  the  wall  to  prevent  overturning.  They  differ  in  the  way  in  which 
the  face  wall  is  attached  to  the  base. 

A  cantilever  wall  is  shown  in  Fig.  65,  consisting  of  a  vertical  stem 
attached  to  a  base,  ACFB.  The  weight  of  the  mass  of  earth  BFEG, 
rests  upon  the  base  of  the  wall  BF  and  serves  to  assist  the  wall  in 
resisting  the  overturning  moment  of  the  earth  thrust.  The  hori- 


230 


RETAINING  WALLS 


zontal  pressure  of  earth  on  EF  is  carried  by  the  vertical  stem  CDEF 
acting  as  a  cantilever  beam.  The  projecting  bases  FB  and  AC  are 
also  cantilever  beams,  the  one  supporting  the  weight  of  earth  resting 
upon  it,  the  other  resisting  the  upward  thrust  of  the  foundation  at 
the  toe  of  the  wall. 

A  counterforted  wall  is  shown  in  Fig.  66.  The  face  wall  CDEF 
is  connected  with  the  base  ACFB  by  narrow  counterforts  EFB, 
spaced  several  feet  apart.  The  counterforts  are  cantilever  beams, 
each  carrying  the  horizontal  earth  thrust  on  the  face  wall  EF  for  a 
panel  length  of  wall.  The  face  walls  CDEF  are  slabs  holding  the 
earth  pressure  between  counterforts  and  transferring  the  pressure 


A       /_  B 

FIG.  65.— Cantilever  Wall. 


FIG.  66.— Counterfort  Walls. 


to  the  counterforts.  The  base  FB  is  a  slab  carrying  the  weight  of 
earth  FEGB  beween  counterforts  and  holding  down  the  ends  of  the 
counterforts.  The  base  AC  at  the  front  of  the  wall  is  a  cantilever 
carrying  the  upward  thrust  of  the  foundation  at  the  toe  of  the  wall. 

The  cantilever  type  is  commonly  used  for  moderate  heights  of 
wall.  For  walls  more  than  20  or  25  feet  high,  the  counterforted  wall 
is  usually  more  economical.  The  quantities  of  materials  required 
for  a  counterforted  wall  are  less  and  the  amount  of  form  work  more 
than  for  a  cantilever  wall. 

130.  Design  of  Cantilever  Wall.— In  designing  reinforced  con- 
crete walls,  the  thrust  in  the  vertical  section  of  earth  passing  through 
the  inner  edge  of  the  base  may  be  computed  by  Rankine's  formula, 
as  given  in  Section  123: 


REINFORCED  CONCRETE  WALI£  231 

eS2          .  cos  i—  Vcos2z  —  cos2<^  eS2  „ 


cos  i  +  V 


— 


(2) 


Values  of  K  may  be  taken  from  Table  XVIII.  This  thrust  is  parallel 
to  the  upper  surface  of  the  earth  and  its  horizontal  and  vertical 
components  are 

eS2  eS2 

H  =  E  cos  i  =  —  K  cos  i,  and  V  =  E  sin  i  —  —  K  sin  i. 

—  2^ 

The  method  of  design  will  be  illustrated  by  numerical  examples. 
Example  3.  —  Design  a  retaining  wall  to  hold  a  level  bank  of  earth 

16  feet  high.     The  base  of  footing  is  to  be  3  feet  below  surface  of 
ground  and  the  pressure  on  the  soil  is  limited  to  4000  lb./ft.2     The 
backing  is  ordinary  soil  with  angle  of  friction  of  35°.     Earth  weighs 
100  pounds  and  concrete  150  pounds  per  cubic  foot.     Unit  stresses 
will  be  based  upon  use  of  2000  pounds  concrete  and  plain  bars  of 
medium  steel. 

Solution.  —  Assume  the  base  under  the  wall  12  inches  thick. 
The  height  of  the  wall  above  the  base  is  then  18  feet,  and  the  hori- 
zontal thrust,  taking  K  from  Table  XVIII, 

„    eS2K     100X18X18X27 

E=          =—  -  -  —  -  =4374  pounds  per  foot  of  length  of  wall. 

z  _ 

The  bending  moment  caused  by  this  thrust  upon  the  section  at 
the  top  of  the  base  is  M=  4374X6X12  =  3  14928  in.-lb. 
From  Table  VII,  for 

fe  =  650  and  f,  =  16,000,  we  find  R  =  108  and  p  =  .0078. 
Then 

Rbd2  =  M  becomes  108X12d2  =  314928,  and  d=15.5  inches. 

Assuming  the  steel  to  be  embedded  1.5  inches  in  the  concrete,  the 
total  thickness  of  the  vertical  stem  at  the  top  of  the  base  will  be 

17  inches. 

The  steel  area  required  for  a  length  of  12  inches  of  wall  is 

'pbd=.  0078X12X15.5  =  1.45  in.2 

From  Table  XV  we  find  that  f-inch  bars  spaced  5  inches  apart  will 
answer  the  purpose. 

If  we  assume  10  inches  to  be  the  minimum  allowable  thickness 
at  the  top  of  the  wall  and  make  the  faces  of  the  wall  plane  surfaces, 
the  thickness  at  all  intermediate  points  will  be  greater  than  required 
for  strength.  At  a  point  12  feet  below  the  top,  the  bending  moment 


232  RETAINING  WALLS 

is  314928X8/27  =  93312  in.-lb.,  and  the  effective  depth  of  beam  is 
13  inches.     Then 

qqqio 


and  from  Table  IX,  we  find  p  =  .0032.  The  area  of  steel  required 
is  12  X  13  X.  0032  =  0.5  in.2  per  foot  of  length,  or  about  one  -third  of 
that  at  the  base.  Similarly  at  a  section  6  feet  below  the  top,  no 
steel  would  theoretically  be  required. 

If  ajl  of  the  bars  be  carried  up  6  feet,  every  third  bar  12  feet  and 
every  sixth  bar  to  the  top  the  reinforcement  will  be  amply  strong. 
The  lower  ends  of  these  bars  should  be  turned  up  in  the  base  for 
anchorage. 

The  maximum  shear  in  section  at  base  is  4374  pounds,  and 

V  4374 

"  =  P=12X.  874X15.  5  =  27  lb'/m' 

No  diagonal  tension  reinforcement  is  necessary. 

Overturning  Moment.  —  Assume  the  width  of  base  at  about  45 
per  cent  of  the  total  height,  or  8.5  feet.  Let  the  inner  surface 
of  the  vertical  stem  be  vertical,  and  place  the  stem  at  a  distance 
equal  to  one-third  the  width  of  base  (6/3)  from  the  toe  of  the  wall. 
(See  Fig.  67.) 

The  moment  of  the  thrust  about  the  toe  at  A  tends  to  overturn 
the  wall,  while  the  moments  of  the  weights  of  the  wall  and  earth 
resting  upon  it  resist  overturning. 

The  weight  of  the  vertical  stem  is 


W  i  =  (18  X  150)  =  3035  pounds. 


The  weight  of  the  base  is  W2  =  1.0X8.5X  150=  1275  pounds. 
The  weight  of  the  earth  is  G=  18X4.25X100  =  7650  pounds. 

rro.  rr    eS2K     100  X  19  X  19  X.  27     ,0_0 

The  earth  thrust,  E  =          =  —  —  =  4873  pounds. 

2i  — 

The  moment  on  the  toe  at  A  is 

Af  =  3035X3.65  +  1275X4.25+7650X6.4-4873X6.33  =  34610  ft.-lb. 
The  point  of  application  of  the  resultant  on  the  foundation  soil  is 
equal  to  the  moment  about  A  divided  by  the  vertical  component 
of  the  resultant,  or 

34610  _2£0fcc 

"3035+1275+7650" 

This  brings  the  resultant  within  the  middle  third  of  the  base. 


REINFORCED  CONCRETE  WALLS 


233 


The  factor  of  safety  against  overturning  is 

3035X3.65+1275X4.25+7650X6.4 


2.12. 


4873X6.33 

Pressure  on  Foundation. — The  total  vertical  load  on  the  foun- 
dation is  3035+1275+7650=11,960  pounds.     The  pressure  at  the 


E  F 


If?     "a 

FIG.  67. — Design  of  Cantilever  Wall. 

toe  is  twice  the  average  pressure,  2X11960/8.5  =  2814  lb./ft.2,  which 
is  within  safe  limits. 

Inner  Base  Cantilever. — The  length  of  the  inner  cantilever  is 
4.25  feet.     It  is  subject  to  the  action  of  three  loads: 

(1)  The  weight  of  the  earth  resting  upon  it  (1800  pounds 
per  linear  foot) ; 

(2)  Weight  of  the  cantilever  itself  (150  pounds  per  linear 
foot). 


234  RETAINING  WALLS 

(3)  Upward  pressure  of  the  foundation  soil  (which  is  0  at 
the  end  D  and  1400  pounds  where  the  cantilever  joins 
the  vertical  wall  at  C). 
The  bending  moment  on  the  section  at  C  is 


=  13,396  ft.-lb.   or   160,752  in-lb. 
From  Table  VII,  R  =  108  and  p  =  .0078.     Then 

108  Xl2d2  =  160752  and  rf=11.2  inches. 

If  the  steel  be  placed  1.75  inches  below  the  top  surface  the  thick- 
ness at  C  is  13  inches, 

A  =pbd  =  .  0078X11.2X12=  1.05  in.2 

From  Table  XV,  we  find  that-f-inch  bars  spaced  5  inches  apart, 
the  same  as  the  vertical  reinforcement  will  answer  the  purpose. 
These  bars  should  be  anchored  by  bending  or  by  continuing  them 
through  the  concrete  on  the  front  of  the  base  to  a  length  of  at  least 
50  diameters  (37.5  inches). 
The  shear  in  section  at  C  is 

7=  1800X4.25+150X4.25-  1400X4.25/2  =  5312  pounds, 

V  5312 

and       *  =       = 


This  value  is  rather  large  for  use  without  diagonal  tension  reinforce- 
ment.   If  we  make 


Iz.b  in. 

Using  d=13  inches  and  embedding  the  steel  2  inches  in  the  con- 
crete, the  total  depth  of  base  at  C  becomes  15  inches. 

Outer  Base  Cantilever. — The  length  of  the  outer  cantilever  is 
2.83  feet.  The  forces  acting  upon  it  are  its  own  weight  acting  down- 
ward, and  the  thrust  of  the  foundation  soil  acting  upward  (2814 
lb./ft.2  at  A  and  1876  lb./ft.2  at  B).  The  shear  in  section  at  B  is 

F  =  2814+187_6283_150x283  =  62121b_ 

If  the  unit  shear  be  limited  to  40  lb./in.2, 
V  6212 


Making  d=  15  inches,  the  total  depth  of  base  at  B  is  17  inches. 


REINFORCED  CONCRETE  WALLS  235 

The  bending  moment  at  B  is 


or  150,120  in./lb. 

•**  ~  J^72  =  10\/10\/1  C  =  55.6, 


R/fs  =  55.6/ 16000  =  .0035. 

From  Table  IX,  p  =  .0038,  and  A  =  .0038X12X15  =  .68  in.2  per  foot 
of  length  of  wall. 

From  Table  XV,  f-inch  bars  will  answer  if  spaced  like  the  other 
reinforcement  5  inches  apart.  These  bars  must  extend  into  the  base 
a  distance  of  at  least  50  diameters  (31  inches)  past  the  section  at  B. 

Horizontal  bars  should  be  placed  longitudinally  through  the 
wall  near  the  exposed  face  to  prevent  cracking  due  to  contraction; 
J-inch  bars  spaced  12  inches  apart  are  sufficient  for  this  purpose. 

Example  4. — A  cantilever  wall  is  to  be  17  feet  high  above  ground 
and  to  support  a  bank  of  earth  whose  surface  has  an  upward  slope 
of  2  horizontal  to  1  vertical  from  the  top  of  the  wall.  Angle  of 
friction  for  backing  earth  0  =  35°.  The  soil  under  the  base  may  be 
safely  loaded  with  6000  pounds  per  square  foot.  Earth  filling  weighs 
100  lb./ft.3  and  concrete  150  lb./ft.3  Safe  values  of  /c  =  500  lb./in.2 
/,=  16,000  lb./in.2,  and  for  diagonal  tension  v  =  30  lb./in.2  n=15. 
The  base  of  the  wall  will  extend  4  feet  below  the  surface  of  the  ground 
and  the  toe  of  the  wall  cannot  extend  beyond  its  face. 

Solution. — Assume  a  depth  of  base  of  24  inches  and  a  width  of 
base  of  12  feet.  (See  Fig.  68.) 

Vertical  Wall. — The  total  height  of  the  vertical  wall  is  19  feet. 
The  thrust  on  the  back  of  this  wall  is 

v    eWK     100X19X19X.39 

E  =  —^-=  —  =  7040  pounds. 

This  acts  parallel  to  the  surface  of  the  earth  and  its  horizontal  com- 
ponent £T  =  7040  cos  26°  30'  =  6300  pounds.  The  moment  of  this 
about  the  base  of  the  wall  is  (6300  X 19/3)  X 12  =  478,800  in.-lb. 
From  Table  VII,  R  =  72  and  p  =  .005.  12d2 = 478800/72  =  6648,  and 
d  =  24  inches. 

The  total  thickness  at  base  is  26  inches.  Take  top  as  12  inches 
thick,  and  make  face  of  wall  vertical.  At  base,  A  =  24X12X.005 
=  1.44  in.2  From  Table  XV,  f-inch  square  bars  4|  inches  apart 
will  answer.  All  bars  will  extend  to  12  feet  below  top,  every  third 
bar  to  6  feet  below  top  and  every  sixth  bar  to  top  of  wall. 


236  RETAINING  WALLS 

Shear  at  base  section  is  6300  pounds  and 
6300 


which  is  within  limits  without  diagonal  tension  reinforcement. 

Overturning  Moment.  —  The  thrust  on  the  vertical  section  at  the 
inner  edge  of  the  base  is 

eS2  v     100X26.  5X26.  5W 
E  =  -^-K  =  -  jr  -  X  .39  =  13,690  pounds. 

2  Z 

Its  horizontal  component  is 

H=  13,690  cos  26°  30'  =  12,250  pounds 
and  its  vertical  component 

V  =  13,690  sin  26°  30'  =  6100  pounds. 
The  weight  of  the  base  of  wall 

TFi  =  12  X  2  X  150  =  3600  pounds. 
Weight  of  vertical  wall 

W2  =  ^~Y^  X  19  X  150  =  4560  pounds. 
Weight  of  earth  on  wall 

<jU  /3L8+!!X19+11X6.6J  X100=22785  pounds. 

The  moment  of  E  about  the  toe  of  the  wall  is 

Mo  =  12250  X  26.5/3  -  6100  X  12  =  35000  ft.-lb. 

The  moment  of  resistance  is 

Mr=3600X6+4560X.64+22785X7.0=  184000  ft.-lb. 

The  factor  of  safety  against  overturning  is  184000/35000  =  5.2. 

The  distance  from  toe  to  point  of  application  of  resultant  pres- 
sure on  foundation 

184000-35000 
3600+4560+22785+6100 

The  maximum  pressure  on  the  soil  at  the  toe  of  the  wall  is 
/3600+4560+22785+6100\2  = 

\  LZ  J 


REINFORCED  CONCRETE  WALLS 


237 


Base  Cantilever. — The  weight  of  earth  resting  upon  the  inner 

base  is 

(q  cv4  Q\ 
9.8X19.6+-  ^p-jx  100  =  21610  pounds. 

The  weight  of  the  base  is  9.8X2X150  =  2940  pounds.     The  upward 

thrust  of  the  soil  is 

CCK 

X 9.8  =  24770  pounds. 


FIG.  68.— Cantilever  Wall. 
The  maximum  bending  moment  at  junction  with  vertical  wall 

M=  ^21610X5.1+2940X4.9-24770X^  X12  =  524,000  in.-lb. 


=  24-6  inches.     Make  full  depth  27  inches. 


A=24.6Xl2X.005  =  1.43in.2;  f -inch  square  bars  spaced 4J  inches 
apart  as  in  vertical  wall  meet  the  requirement. 

For  this  loading,  the  point  of  maximum  shear  occurs  where  the 
intensity  of  the  downward  forces  equals  that  of  the  upward  forces. 
This  occurs  at  a  point  distant 


5055 -(1960+300) 
516+50 


4.94  feet 


238  RETAINING  WALLS 

from  the  back  of  the  vertical  wall.     The  shear  at  this  point  is 

24-5+22-0V.86X100+2x4.86X150-2508 


X4.86  =  6663  pounds 
and 

V  6663 


The  reinforcing  bars  must  be  anchored  and  longitudinal  bars 
introduced  to  prevent  cracking  as  in  Example  3. 

131.  Design  of  Counterforted  Walls. — In  walls  of  the  counter- 
forted  type,  the  vertical  curtain  wall  (See.  Fig.  69)  is  a  slab  supported 
against  the  horizontal  thrust  of  the  earth  by  the  counter- 
forts at  frequent  intervals.  The  counterforts  are  cantilever  beams 
held  in  place  by  the  base,  and  each  carrying  a  panel  load  of  the  thrust 
against  the  vertical  slab.  The  inner  base  is  a  horizontal  slab,  sus- 
pended from  the  counterforts,  and  carrying  the  weight  of  earth  resting 
upon  it.  The  outer  base  is  a  cantilever  and  carries  the  upward  pres- 
sure of  the  soil  upon  the  toe  of  the  wall  as  in  the  cantilever  wall. 

Example  5. — A  wall  with  counterforts  is  to  support  a  bank  of 
earth  23  feet  high,  carrying  a  double  track  railway  as  shown  in  Fig. 
69.  The  base  of  the  wall  will  extend  4  feet  below  the  surface  of 
the  ground,  and  the  soil  is  capable  of  carrying  a  load  of  7000  lb./ft.2 
The  filling  is  to  be  of  ordinary  earth  with  0  =  35°,  e=  100  lb./ft.2,  and 
w=150  lb./ft.2.  Maximum  allowable  stresses  are  /c  =  650  Ib./in.2, 
/s=  16,000  Ib./in.2,  and  #=120  Ib./in.2,  or  without  diagonal  tension 
reinforcement  v  —  4Q  Ib./in.2.  ft  =15. 

Solution. — For  heavy  locomotive  loads,  the  surcharge  should  be 
taken  as  L=1000  pounds  per  square  foot  of  surface. 

The  distance  apart  of  counterforts  may  vary  with  different  con- 
ditions and  should  be  carefully  examined  in  each  instance  as  to  its 
effect  upon  the  cost  of  the  wall.  In  this  problem,  we  will  assume 
a  distance  c.  to  c.  of  counterforts  of  8  feet.  Also  try  a  thickness  of 
counterforts  of  18  inches. 

Vertical  Walls. — Assuming  the  base  of  the  wall  to  be  2  feet 
thick  the  height  of  the  curtain  wall  is  23+4  —  2  =  25  feet.  If  we 
divide  the  vertical  slab  into  strips  each  1  foot  high,  the  horizontal 
thrust  against  the  bottom  strip  will  be  (taking  K  from  Table  XVIII), 

(eh+L)K  =  (100X25+ 1000). 27  =  945  lb./ft.2 
This  strip  is  then  a  horizontal  beam  supported  at  intervals  of  8  feet, 


REINFORCED  CONCRETE  WALLS  239 

and  carrying  a  uniform  load  of  945  pounds  per  linear  foot.     Con- 
sidering it  to  be  a  partly  continuous  beam, 


M       72576 
d  =      = 


Make  d  =  S  inches,  and  the  total  thickness  10  inches.  As  10  inches 
is  about  the  minimum  thickness  allowable  at  the  top  of  the  wall, 
make  the  thickness  the  same  for  the  whole  slab. 

For    the    bottom    strip    with   d  =  S  inches,   jg=  0     0     Q  =  95, 

l^XoXo 

R/fs  =  95/16000  =.0059,  and  from  Table  IX,  p  =  .0068. 
A  =  .0068X12X8  =  .65  in.2, 

and  from  Table  XV  we  find  that  f-inch  round  bars,  spaced  5  inches 
apart  will  answer. 

For  a  strip  16  feet  below  the  top  of  the  wall, 

,,    702X8X8X12  .  53914 

-        =53914  m.-lb.,     £ 


p  =  .0049,  A  =  .47  in.2  and  the  f-inch  bars  are  needed  7  inches  apart. 
At  8  feet  below  the  top, 

,,    486X8X8X12  .     „ 

M  =  -  JQ  -  =  31104  m.-lb., 

R  =49,  p  =  .0034,  A  =  .33  in.2  and  the  f-inch  round  bars  may  be  spaced 
10  inches  apart. 

We  will  therefore  use  f-inch  round  bars  spaced  5  inches  apart  for 
the  lower  9  feet,  7  inches  apart  for  the  next  8  feet  and  10  inches  apart 
in  the  upper  8  feet  of  the  curtain  wall.  These  bars  will  be  run  2  inches 
from  the  face  of  the  wall,  and  negative  moments  at  the  counterforts 
will  be  taken  care  of  by  short  rods  of  the  same  diameter  and  spacing 
extending  24  inches  on  each  side  of  the  mid-section  of  the  counterfort. 

The  span  for  shear  is  the  clear  distance  between  counterforts. 
Assuming  the  counterfort  to  be  18  inches  thick,  the  maximum  shear 
is  V  =  (4  -  0.75)  X  945  =  3070  lb./in.2,  and  the  unit  shear 

3070 


The  8-inch  thickness  is  therefore  sufficient  without   reinforcement 
for  diagonal  tension. 


240  RETAINING  WALLS 

Resistance  to  Overturning.  —  Assume  the  width  of  base  at  about 
50  per  cent  of  the  total  height  or  13.5  feet,  and  place  the  middle 
of  the  vertical  wall  over  a  point  one-third  the  width  from  the  toe. 
Taking  a  foot  of  length  of  wall  between  counterforts,  the 

weight  of  certain  wall  =  150  X  25  X  10/  12  =  3  125  pounds, 

weight  of  base  =  150  X  2  X  13  .  5  =  4050  pounds, 

weight  of  earth  =  100  X  25  X  8.6  =  21500  pounds, 

weight  of  load  upon  surface  =1000X8.6  =  8600  pounds. 

Using  Rankine's  formula, 

X.27=  17131  pounds. 


The  moment  of  E  about  the  toe  of  the  wall  is 

Mo  =  17131  X9  =  154179  ft.-lb., 
and  the  moment  of  resistance 

Mr  =  3125X4.5+4050X6.75+(21500+8600)X9.2  = 

The  factor  of  safety  against  overturning  is  322919/154179  =  2.09. 
The  distance  from  the  toe  of  the  wall  to  the  point  of  application 
of  the  resultant  pressure  is 

322919-154179     _         , 

X    3125+4050+30100  ' 

> 

and  is  within  the  middle  third  of  the  base. 

Pressure  on  Soil.  —  As  the  resultant  cuts  the  bottom  of  the  base 
at  one-third  the  width  from  the  toe,  the  maximum  pressure  at  the 
toe  is 


The  pressure  at  the  inner  edge  of  the  base  will  be  practically  nothing. 

Inner  Base  Slab.  —  The  loading  on  the  horizontal  base  slab  is 
the  difference  between  the  sum  of  the  weights  of  earth  and  of  the 
base  acting  downward,  and  the  soil  pressure  acting  upward.  The 
maximum  load  will  be  at  the  inner  edge,  where  the  upward  pressure 
is  a  minimum.  Taking  a  foot  in  width  along  this  edge  and  neglect- 
ing the  upward  pressure,  the  load  will  be  1000+25X100+2X150 
=  3800  pounds  per  linear  foot. 

The  thickness  of  base  slab  will  probably  be  determined  by  require- 
ments for  shear.  The  maximum  shear  at  edge  of  counterfort  (taking 


REINFORCED  CONCRETE  WALLS  241 

counterforts  as  18  inches  thick)  is  V  =  3800(4  -.75)  =  12350  pounds, 
and  if  no  reinforcement  be  used  for  diagonal  shear,  the  depth 

,     V  12350 


or  the  full  depth  must  be  32  inches.     If  the  assumed  depth  of  24 
inches  be  used, 

12350  ,. 


This  would  require  light  reinforcement  for  diagonal  shear  for  8 
inches  from  the  edge  of  the  counterfort  and  may  be  met  by  bending 
up  a  part  of  the  tension  reinforcement  to  use  for  negative  moment 
over  the  supports. 

The  bending  moment  in  the  base  slab  is 


and  using  the  24-inch  depth 

270480 
"12X22X22" 


Table  VII  gives  p  =  .0032,  and  A  =  .0032X22X12  =  .85  in.2  From 
Table  XV,  we  find  that  j-inch  round  bars  spaced  6  inches  apart  are 
needed.  The  negative  moments  at  the  counterforts  are  the  same 
as  the  positive  moments  and  may  be  provided  for  by  bending  up 
alternate  bars  on  each  side  of  the  support,  and  extending  these  across 
the  counterforts  to  the  quarter  points  in  the  next  panel. 

Counterforts.  —  The  counterforts  act  as  cantilevers  to  carry  the 
horizontal  thrust  upon  the  curtain  wall  for  panel  lengths  of  8  feet. 
This  thrust  is 

pounds? 


and  its  moment  about  the  section  at  the  top  of  the  base  is 

OK 

M=  110700X^X12  =  11070,000  in.-lb. 

o 

Considering  the  counterfort  to  act  as  a  T-beam,  of  which  the 
curtain  wall  is  the  flange,  and  the  resultant  of  the  compressive 
stresses  to  act  at  the  middle  of  the  base  of  the  curtain  wall,  we  may 
take  this  middle  point  as  the  center  of  moments  for  the  tensions 
in  the  steel  in  the  back  of  the  counterfort.  If  the  center  of  gravity 


242 


RETAINING   WALLS 


of  the  steel  is  3  inches  from  the  surface  of  the  concrete,  its  lever 
arm  is  8.1  feet,  and  the  total  stress  in  the  steel  is 


pounds. 


8.1X12 


The    required    steel    area   is  A  =  114000  16000=7.  12  in.2     1 
Table  X,  we  find  that  six  11-inch  round  bars  will  answer.    These 
may  be  placed  in  two  rows,  four  bars  being  placed  2  inches  and  two 
bars  5  inches  from  the  surface  of  the  concrete.    These  may  be  spaced 


FIG.  69.— Design  of  Counterfeited  Wall. 

4  inches  apart  and  3  inches  from  the  sides  in  a  thickness  of  counter- 
fort of  18  inches. 

At  a  section   16  feet    below  the  top  the  moment  =4718900 
in.-lb.,  and  the  steel  required 


4718000 


5.4X12X16000 


=  4.54  in.2 


At  8  feet  below  the  top  M=  1327100  in.-lb.  and  A  =2.46  in.2  Two 
bars  may  be  stopped  at  16  feet  below  the  top,  two  at  8  fcvt  and 
the  others  extend  to  the  top  of  the  counterfort. 


REINFORCED  CONCRETE  WALLS  243 

The  total  shear  in  base  section  of  counterfort  is  110,700  pounds, 
and 

V  110700 


At  16  feet  below  the  top  v  =  45  lb./in.2  Reinforcement  for  diagonal 
tension  is  needed  from  the  base  to  a  little  above  the  section  16  feet 
below  the  top.  This  may  be  provided  by  the  bars  to  be  used  for 
bonding  the  counterforts  to  the  curtain  walls  and  base  slabs. 

Bonding  Bars. — The  curtain  wall  and  the  base  slab  must  be  tied 
to  the  counterforts  by  horizontal  and  vertical  bars  capable  of  carry- 
ing the  reactions  at  the  points  of  support.  These  will  equal  the  sum 
of  the  shears  on  the  two  sides  of  the  counterfort.  At  the  bottom 
of  the  curtain  wall  the  load  per  foot  of  height  is  2(4  — .75)945  =  6140 
pounds  and  the  area  of  steel  required  6140/16000=  .38  in.2  If  these 
bars  be  placed  in  pairs  and  at  the  same  distance  apart  as  the  hori- 
zontal reinforcement  in  the  curtain  walls,  ^-inch  round  bars  will 
answer.  These  should  be  looped  around  the  steel  in  the  face  of 
the  curtain  wall,  and  extend  into  the  counterfort  at  least  50  diameters 
for  bond  strength. 

For  the  base  slab,  the  load  upon  the  bonding  bars  per  foot  of 
width  2(4 -.75)3600  =  23,400  pounds,  and  the  area  of  steel  required 
A  =  23400/16000  =  1.46  in.2  A  pair  of  f-inch  square  bars  spaced 
6  inches  apart  meets  this  requirement. 

Base  Cantilever. — The  projection  of  the  base  at  the  toe  of  the 
wall  is  a  cantilever,  as  in  the  cantilever  wall,  and  carries  the  upward 
thrust  of  the  soil.  The  maximum  shear  is 

F=  /5270+3830\  X3.7-300X3.7  =  15725  pounds. 
15725 


This  cantilever  may  be  made  39  inches  at  the  face  of  the  curtain 
wall  and  taper  to  12  inches  at  the  toe. 

The  maximum  moment  is  M  =  15725  X  2  X  12  =  377400, 

377400 
12X37X37 

R/fs  =  23/16000  =  0014,  and  from  Table  IX,  p  =  .0015.  A  =  .0015  X  12 
X37  =  .67  in.2,  and  from  Table  XV,  |-inch  bars  spaced  5  inches 
apart  may  be  used. 


244  RETAINING  WALLS 


ART.   36.     CONSTRUCTION   OF  RETAINING  WALLS 

132.  Foundations. — As  stated  in  Section  126,  the  most  common 
cause  of  failure  of  retaining  walls  is  defective  foundations.     Careful 
attention  must  always  be  given  to  the  sufficiency  of  the  foundation, 
footings  being  arranged  so  that  excessive  pressure  does  not  come  upon 
the  soil  upon  which  the  structure  rests. 

On  compressible  soils  it  is  important  to  equalize  the  pressures 
so  that  settlement  under  the  toe  of  the  wall  may  not  cause  the  wall 
to  tip  forward.  In  constructing  gravity  walls  this  is  accomplished 
by  using  a  footing  under  the  main  wall  which  extends  sufficiently 
beyond  the  base  of  the  wall  to  cause  the  pressures  to  be  equalized 
over  the  foundation  soil,  and  bring  the  resultant  near  the  middle  of 
the  foundation.  Reinforced  concrete  walls  must  be  given  sufficient 
base  to  prevent  excessive  pressures  on  the  foundation  soil. 

The  extension  of  the  front  base  cantilever  may  often  be  used  as  a 
means  of  securing  good  distribution  of  pressures  upon  the  founda- 
tion; when  this  is  not  feasible,  widening  the  base  at  the  back  of  the 
wall  may  answer  the  same  purpose. 

When  the  soil  is  compressible,  there  is  always  some  settlement,  and 
this  is  greatest  where  the  load  is  greatest.  In  many  instances,  there- 
fore, it  may  be  advisable  to  extend  the  footing  sufficiently  to  bring 
the  center  of  pressure  back  of  the  middle  of  the  foundation  so  as  to 
make  the  pressure  greater  at  the  heel  than  at  the  toe  of  the  wall,  and 
produce  a  tendency  to  tilt  backward. 

When  soft  materials  are  encountered,  or  when  the  pressures  cannot 
be  safely  distributed  over  the  foundation  soil,  a  pile  foundation  or 
some  other  means  of  securing  firm  support  for  the  wall  must  be  em- 
ployed. Methods  of  constructing  such  foundations,  and  the  loads 
which  may  be  borne  by  soils  are  discussed  in  Chapter  XII. 

The  depth  of  foundations  should  be  sufficient  to  prevent  freezing 
in  the  soil  under  the  footing  of  the  walls,  or  of  the  earth  in  front  of  the 
wall  at  the  depth  of  the  bottom  of  the  footing.  This  usually  requires 
that  the  footing  extend  from  3  to  5  feet  below  the  surface  of  the 
ground,  depending  upon  local  and  climatic  conditions. 

133.  Drainage  and  Back-Filling. — Failures  of  retaining  walls  have 
frequently  occurred  because  of  the  lack  of  proper  drainage,  hence  pro- 
vision should  always  be  made  for  the  ready  escape  of  water  from  the 
earth  behind  the  wall.     If  the  water  is  held  in  and  the  back-filling 
becomes  saturated,  the  weight  of  the  material  is  increased  and  ~the 
angle  of  friction  decreased,  thus  producing  a  much  heavier  pressure 


CONSTRUCTION  OF  RETAINING  WALLS 


245 


against  the  wall.  Freezing  of  wet  material  behind  the  wall  may  also 
produce  dangerous  pressures  against  the  back  of  it. 

To  provide  for  drainage,  weep-holes  are  commonly  left  through 
the  base  of  the  wall  at  intervals  of  10  or  15  feet.  In  concrete  walls, 
these  are  usually  made  by  the  use  of  drain  tile  about  3  inches  in 
diameter.  In  stone  masonry  walls,  the  stones  are  set  so  as  to  leave  an 
opening  2  or  3  inches  wide  through  the  course  of  masonry  at  the  base 
of  the  wall. 

When  the  back-filling  is  of  retentive  material  through  which 
water  will  not  readily  pass,  a  layer  of  cinders,  gravel,  or  some  other 
porous  material  should  be  placed  against  the  back  of  the  wall  to  per- 


FIG.  70. — Gravity  Wall  of  Concrete 

mit  the  water  to  reach  the  drains  without  difficulty.  It  is  always 
important  that  water  be  not  held  in  the  back-filling. 

The  manner  of  placing  the  back-filling  may  sometimes  have  an 
important  effect  upon  the  pressures  against  the  wall.  The  layers  in 
which  the  filling  is  placed  should  slope  away  from  the  wall.  With 
some  materials,  there  is  a  tendency  for  the  earth  to  slide  along  the 
surfaces  between  the  layers  in  compacting  and  settling  into  place, 
which  may  materially  increase  the  pressure  if  inclined  toward  the 
wall. 

134.  Gravity  Walls. — In  constructing  gravity  walls  it  is  common 
to  give  the  back  of  the  wall  a  batter  by  stepping  off  the  surface,  thus 


246  RETAINING  WALLS 

widening  the  base  and  making  a  smaller  projection  of  footing  neces- 
sary. In  walls  of  stone  masonry,  the  steps  are  usually  the  height  of 
one  or  more  courses  while  in  plain  concrete  walls  the  steps  are  usually 
of  uniform  height  of  2  to  4  feet,  to  simplify  the  form  work,  and  for 
convenience  in  placing  the  concrete.  Fig.  70  shows  a  typical  section 
for  a  wall  of  this  kind,  as  used  for  carrying  a  railway  embankment. 

It  is  common  to  batter  the  back  of  a  masonry  wall  at  the  top  for 
3  or  4  feet  (see  Fig.  70)  to  prevent  injury  if  the  backing  becomes 
frozen  near  the  surface  and  is  lifted  by  the  expansion.  This  is 
known  as  frost  batter,  and  is  commonly  2  or  3  inches  to  the  foot. 

Concrete  is  quite  largely  replacing  stone  masonry  in  the  construc- 
tion of  retaining  walls.  For  high  walls,  reinforced  concrete  is  econom- 
ical and  usually  employed,  while  for  walls  less  than  20  or  25  feet 
high,  gravity  walls  may  often  be  less  expensive  than  reinforced  walls. 
A  larger  quantity  of  concrete  is  required  for  the  gravity  wall,  but 
concrete  of  less  rich  character  may  be  employed  and  no  steel  is  needed. 
For  reinforced  walls,  about  1  to  6  concrete  is  usually  used  for  the  body 
of  the  work,  while  1  to  9  concrete  may  commonly  be  used  for  gravity 
walls;  footings  being  made  of  1  to  11  or  1  to  12  mixtures.  The  cost 
of  forms  does  not  vary  greatly  for  the  two  types  of  wall. 


CHAPTER  VIII 
MASONRY  DAMS 

ART.  37.    GRAVITY  DAMS 

135.  Stability  of  Dams. — A  gravity  dam,  like  a  retaining  wall, 
depends  upon  the  weight  of  the  mass  of  masonry  to  resist  the  thrust 
of  the  water  against  it.  As  the  dam  carries  water  pressure  instead 
of  earth  pressure,  the  loads  to  which  the  dam  is  subjected  are  defi- 
nitely known,  and  the  thrusts  are  everywhere  normal  to  the  surfaces 
of  contact. 

Let  A  BCD,  Fig.  71,  represent  a  slice,  1  foot  thick,  of  a  gravity 
dam  sustaining  a  head  of  water  as  shown. 


FIG.  71. 

h  =  height  of  water  above  section  AB; 
H  =  horizontal  pressure  of  water  against  the  dam; 
V  =  vertical  pressure  of  water  on  back  of  dam; 
W  =  weight  of  dam  above  section  AB', 
R  =  resultant  pressure  upon  section  AB', 

k  =  horizontal  distance  from  inner  edge  of  base  to  line  of  action  of  V ; 
6  =  width  of  base  A  B', 

d  =  distance  from  outer  edge  of  base  to  line  of  action  of  W; 

247 


248  MASONRY  DAMS 

x  =  distance  from  outer  edge  of  base  to  point  of  application  of 
resultant  R. 

The  conditions  of  stability  for  the  dam  are  the  same  as  for  the 
retaining  wall: 

It  must  not  slide  or  shear  on  a  horizontal  section. 

It  must  not  overturn  about  outer  edge  of  section. 

The  masonry  must  not  be  crushed  by  pressure  upon  the  section. 

Stability  against  Sliding. — Taking  the  weight  of  water  as  62.5 
lb./ft.3,  the  horizontal  thrust  against  the  dam  above  AB  is  #  =  31.25 
h2.  This  is  the  shear  upon  the  section  AB.  If  AB  is  a  joint  in  the 
dam,  or  the  base  of  the  dam,  H  must  be  resisted  by  the  friction  of  the 
masonry  upon  the  masonry  below,  or  upon  the  foundation  under  the 
dam,  and  the  value  of  H/(W+V)  must  not  exceed  the  coefficient 
of  friction  for  the  material.  If  A  B  is  a  section  in  a  concrete  dam,  H 
is  resisted  by  the  shearing  strength  of  the  concrete  as  well  as  by  the 
friction. 

Continuous  joints  are  not  usually  employed  in  construction  of 
masonry  dams,  and  the  interlocking  of  stones  eliminates  the  tendency 
to  slide  without  shearing  blocks  of  stone.  The  possibility  of  sliding 
need  usually  only  be  considered  at  the  foundation. 

Stability  against  Overturning. — The  overturning  moment  about 
the  outer  edge  of  the  section  at  A,  due  to  pressure  of  water,  is 

M0=  ~X 

o 

The  resisting  moment  of  the  weight  of  wall  is  Mr  =  Wd,  and  the  dis- 
tance from  the  outer  edge  A  to  the  point  of  application  of  the  resultant 
pressure  on  the  base  is 


W+V  W+V 

If  the  water  face  of  the  dam  is  vertical,  V  =  0  and 


W 


(2) 


Assuming  that  pressures  upon  AB  are  distributed  with  uniform 
variation  from  A  to  B,  x  should  be  greater  than  6/3  in  order  that 
no  tension  may  be  developed  in  the  section,  as  in  the  gravity  retain- 
ing wall. 

Stability  against  Crushing. — The  total  pressure  normal  to  the 
section  AB  is  TF+F,  distributed  over  the  section  with  center  of  pres- 


GRAVITY  DAMS  249 

sure  distant  x  from  A.  The  maximum  normal  unit  pressure  is 
therefore  (see  Section  52) 

/c  =  —     — p—     — •       ......     (3) 

This  is  approximately  the  crushing  stress  in  the  masonry  at  the 
outer  edge  of  the  section,  or  the  maximum  pressure  upon  the  founda- 
tion if  A  B  is  the  base  of  the  dam. 

When  the  reservoir  is  empty  and  the  water  pressure  is  removed, 
the  pressure  upon  the  section  AB  will  be  W,  with  center  of  pressure 
distant  d  from  the  outer  edge.  The  unit  pressure  at  the  outer  edge 
of  the  section  will  be 

/.- 

and  at  the  inner  edge, 


In  dams  of  unsymmetrical  cross-sections  it  is  necessary  to  con- 
sider the  pressures  coming  upon  the  bases  of  sections  when  the  water 
pressures  are  removed,  as  when  the  reservoir  is  empty.  In  this  case, 
the  weight  of  dam  will  be  the  only  load,  and  the  centers  of  pressure 
due  to  this  weight  must  always  come  within  the  middle  third  of  the 
base,  and  the  crushing  stress  be  within  proper  limits,  so  that  removal 
of  the  water  pressure  may  produce  no  harmful  effects  upon  the  dam. 

136.  Graphical  Analysis  of  Profiles  of  Dams. — For  low  dams 
carrying  small  heads  of  water,  trapezoidal  cross-sections  may  be 
employed,  and  designs  made  in  the  same  way  as  for  retaining  walls 
using  water  pressure  instead  of  earth  pressure  upon  the  back  face  of 
the  dam.  As  the  depth  increases  such  a  section  becomes  increasingly 
uneconomical  and  the  form  of  cross-section  should  be  modified  so  as 
to  make  the  thickness  only  that  required  to  carry  the  load  above, 
and  the  profile  such  as  to  distribute  the  material  to  the  best  advan- 
tage. 

Fig.  72  shows  a  method  of  graphical  analysis  applied  to  the  sec- 
tion of  a  gravity  dam.  ookk  represents  a  section  of  a  dam  100  feet 
high.  Take  a  slice  of  the  dam  1  foot  thick  and  of  the  section  shown 
and  divide  this  by  horizontal  planes,  a-a,  b-b}  c-c,  etc.,  into  a  number  of 
horizontal  layers  (in  this  case,  each  10  feet  thick). 

The  weights  of  the  layers,  ooaa,  aabb,  etc.,  are  now  computed  and 
plotted  to  a  convenient  scale,  in  the  vertical  line  0-K.  The  distance 
from  0  to  each  of  the  several  points,  A}  B,  C,  etc.,  represents  the 
total  weight  of  masonry  Wa,  Wb,  etc.,  above  the  corresponding  sec- 
tion a-a,  b-b,  etc.,  of  the  dam. 


250 


MASONRY  DAMS 


The  line  of  action  of  the  total  weight  of  masonry  above  each 
horizontal  section  must  now  be  found.  This  may  be  done  by  taking 
moments  about  a  vertical  line,  or  it  may  be  done  graphically  as 
follows: 


FIG.  72. — Graphical  Analysis  of  Gravity  Dam. 

The  center  of  gravity  of  each  layer  into  which  the  section  of 
the  dam  has  been  divided  is  determined  and  marked  (as  shown  by 
the  points  enclosed  by  circles).  From  the  point  o\,  lay  off  on  the 
line  Oi-ki  the  distances  from  the  centers  of  gravity  of  the  layers  to 
any  vertical  line,  as  o-kf.  (The  scale  used  in  laying  off  these  distances, 
oi  —  ai,  oi  —  bi,  etc.,  is  here  made  larger  than  that  used  for  the  section 


GRAVITY  DAMS  251 

of  the  dam.)  Assume  a  pole,  P,  and  draw  strings  to  the  weight  line 
0-  K,  then  from  a  point  on  the  vertical  through  ki  draw  the  equilib- 
rium polygon  as  shown,  finding  the  positions  of  the  resultant  lines  of 
action,  Wk,  Wi,  Wh,  etc.  The  distances  of  these  lines  from  the 
vertical  through  o\  are  the  same  as  the  distances  of  the  respective 
centers  of  gravity  from  the  line  o-k'  on  the  section  of  the  dam. 
Plotting  these  lines  of  action  and  drawing  them  to  intersection  with 
the  corresponding  horizontal  sections  upon  which  they  act,  we  find 
the  line  of  pressure  for  the  dam  with  no  water  pressure  against  it. 

When  water  pressure  is  against  the  dam  to  its  full  height,  the 
horizontal  against  any  portion  h  feet  in  depth  below  the  surface  is 
#  =  31.25  h2.  These  pressures  may  be  computed  for  each  of  the 
horizontal  sections,  and  each  resultant  pressure  acts  on  a  horizontal 
line  at  one-third  the  height  from  the  section  to  the  surface  of  the 
water,  as  shown,-  Ha,  Hb,  etc. 

On  the  horizontal  line  O-K',  make  the  distances  0-A',  0-5', 
etc.,  equal  the  values  of  the  water  pressures  Ha,  Hb,  etc.,  to  the  same 
scale  as  used  for  the  weights  of  masonry.  The  lines  A- A',  B-B', 
etc.,  now  represent,  in  direction  and  amount,  the  resultant  pressures, 
Ra,  Rb,  Re,  etc.,  upon  the  various  horizontal  sections  aa,  bb,  cc,  etc., 
of  the  dam.  Lines  drawn  parallel  to  these  directions  through  the 
intersections  of  the  corresponding  H  and  W  lines  of  action  give  the 
points  of  application  of  these  resultants  upon  the  various  sections, 
and  locate  the  lines  of  pressure  with  water  against  the  dam  to  the 
top. 

137.  Design  of  Profile. — In  designing  a  profile,  for  a  dam  we  com- 
mence at  the  top  with  the  assumed  thickness  and  find  by  trial  the 
required  base  thickness  for  each  horizontal  layer,  making  each  thick- 
ness such  that  the  line  of  pressure  remains  everywhere  within  the 
middle  third  of  the  section.  This  may  be  done  by  the  use  of  the 
formulas  given  in  Section  135  or  by  the  graphical  method  of  Section 
136. 

The  crushing  stress  upon  the  masonry  must  also  be  kept  within 
safe  limits. 

Let  6  =  the  width  of  the  section; 

x  =  the  distance  from  the  outer  edge  to  the  point  of  appli- 
cation of  R', 

2/  =  the  distance  from  the  inner  edge  to  the  point  of  appli- 
cation of  W. 

The  maximum  crushing  stress  at  the  outer  edge  of  the  section  is 
given  by  the  formula, 

(5) 


252  MASONRY  DAMS 

The  maximum  crushing  stress  at  the  inner  edge  is 

,  _W(4b-6y) 


The  allowable  crushing  stress  depends  upon  the  quality  of  masonry 
used,  and  the  conditions  under  which  the  dam  is  to  be  constructed. 
In  high  dams,  where  the  front  face  of  the  dam  has  considerable 
batter,  the  pressure  allowed  at  the  outer  face  is  often  made  less  than 
that  at  the  inner  face.  The  maximum  pressure  at  the  inner  edge  of 
a  section  occurs  when  the  dam  carries  no  water  pressure,  and  the 
resultant  pressure  on  the  base  is  vertical.  The  maximum  pressure 
at  the  outer  edge  occurs  when  full  water  pressure  is  on  the  dam,  the 
batter  of  the  outer  face  is  greater  than  that  of  the  inner  face,  and  the 
resultant  pressure  is  inclined,  only  its  vertical  component  being  con- 
sidered in  determining  the  stress.  For  these  reasons  Rankine's 
recommendation  that  the  allowable  unit  crushing  stress  at  the 
outer  edge  be  made  less  than  that  at  the  inner  edge  has  been  followed 
by  some  designers.  Pressures  of  from  8  to  15  tons  per  square  foot 
have  been  allowed  in  a  number  of  large  dams  of  massive  rubble  or 
cyclopean  concrete. 

The  profile  resulting  from  this  method  of  design  is  somewhat 
irregular  and  may  be  modified  by  fitting  it  with  more  uniform  batters 
and  smooth  curves,  thus  giving  a  more  pleasing  appearance  and  better 
profiles  for  construction  purposes,  without  appreciably  affecting  its 
stability. 

Vertical  Water  Pressure.  —  As  the  water  face  of  the  dam  is  nearly 
vertical,  it  is  usual  to  disregard  the  vertical  component  of  the  water 
pressure,  which  is  of  small  consequence  in  dams  of  less  than  about  180 
to  200  feet  in  height.  This  component  has  the  effect  of  diminishing 
the  stress  upon  the  outer  edge  of  the  section  while  somewhat  increas- 
ing the  total  pressure.  Its  neglect  is  therefore  a  small  error  on  the 
safe  side  until  a  depth  is  reached  at  which  the  slope  of  the  inner  face 
may  make  it  of  more  importance. 

The  shape  of  the  profile  depends  upon  the  top  width  given  to  the 
dam,  and  the  weight  of  the  masonry  used. 

The  top  width  must  be  sufficient  to  resist  any  probable  wave  action 
and  ice  pressure,  and  should  usually  be  made  greater  for  high  dams 
than  for  low  ones.  This  is  a  matter  of  judgment  in  each  case,  about 
one-tenth  of  the  height  of  dam  being  frequently  used,  with  a  minimum 
of  about  5  feet  and  a  maximum  of  20  feet  where  no  roadway  is  carried 
on  top  of  the  dam. 

The  dam  should  always  extend  to  a  sufficient  height  above  the 


GRAVITY  DAMS  253 

normal  water  surface  to  prevent  water  passing  over  the  dam  due  to 
waves  of  floods  for  which  wasteways  might  not  be  quite  sufficient. 
This  may  require  the  dam  to  be  raised  5  or  10  feet  above  the  eleva- 
tion of  the  expected  water  surface.  In  designing  the  dam,  water 
should  be  assumed  level  with  the  top. 

The  weight  of  masonry  used  in  dam  construction  commonly  varies 
from  about  135  to  150  pounds  per  cubic  foot.  The  heavier  the  masonry 
is  assumed  to  be,  the  less  the  required  width  of  section  until  a  depth 
is  reached  at  which  the  width  is  determined  by  the  necessity  of  pro- 
viding sufficient  area  to  carry  the  weight  of  masonry  above.  Below 
this  point,  usually  about  200  feet  below  the  water  surface,  the  width 
required  is  greater  for  the  heavier  masonry  if  the  same  unit  com- 
pression be  allowed. 

Uplift  and  Ice  Pressure. — If  water  under  hydrostatic  pressure 
has  access  to  the  interior  of  the  dam,  the  upward  pressure  will  tend 
to  lift  the  masonry  and  diminish  its  effective  weight  in  the  moment 
which  prevents  overturning.  In  this  discussion  it  has  been  assumed 
that  the  dam  is  constructed  water-tight,  but  as  this  is  not  altogether 
possible,  in  many  instances  it  may  be  necessary  to  allow  for  upward 
pressure  in  designing  the  profile,  or  make  special  provision  for  drain- 
age— a  topic  discussed  in  Section  140. 

If  ice  forms  on  the  surface  when  the  reservoir  is  full,  a  consider- 
able pressure  may  be  brought  against  the  top  of  the  dam,  which 
should  be  considered  in  its  design.  This  will  be  a  concentrated  hori- 
zontal thrust  at  the  surface  of  the  water  equal  to  the  crushing  strength 
of  the  ice,  and  has  been  assumed  in  a  number  of  important  dams  at 
from  2500  to  4500  pounds  per  linear  foot  of  dam.  In  storage  reser- 
voirs generally,  heavy  ice  is  not  likely  to  occur  with  full  reservoir, 
and  if  water  be  low  when  freezing  occurs  no  special  allowance  for  ice 
pressure  is  necessary.  Local  conditions  must  determine  the  necessity 
of  allowing  for  ice  pressure  in  each  instance. 

138.  Diagonal  Compressions. — The  common  method  of  analysis, 
already  described,  considers  only  the  stresses  upon  horizontal  sec- 
tions and  resolves  the  diagonal  thrusts  into  normal  compressions  and 
parallel  shears  upon  these  sections.  This  method  does  not  give  the 
actual  maximum  compressions,  but  by  using  proper  unit  stresses  has 
seemed  to  give  satisfactory  results  in  use.  Several  methods  have 
been  proposed  for  computing  more  accurately  the  maximum  unit 
compressions. 

Diagonal  Compression  upon  Horizontal  Section. — In  1874  Bou- 
vier *  used  the  actual  diagonal  pressure  (R,  Fig.  72)  in  computing  the 
1  Annales  des  Fonts  et  Chaussees,  1875. 


254 


MASONRY  DAMS 


maximum  unit  compression  upon  a  horizontal  section,  claiming  that 
the  unit  compressive  stresses  produced  by  R  parallel  to  its  line 
of  action  are  greater  than  those  normal  to  the  section.  He  con- 
sidered R  to  be  distributed  along  A-B,  so  as  to  act  upon  successive 
small  sections  normal  to  its  direction  as  shown  in  Fig.  73.  If  /3  is  the 
angle  made  by  R  with  the  normal  to  section  A  —  B,  and  b  is  the  width 
of  section,  the  area  upon  which  R  acts  is  AC=b-coS'@,  and  the  maxi- 
mum intensity  of  the  compressive  stresses  is 


= 

Jcd 


fc 


b2  cos2  |8       cos2  0' 


.     .     (7) 


in  which  fCd  is  the  unit  compression  at  the  outer  edge  of  the  section 
parallel  to  R,  and  fc  is  that  normal  to  the  section  at  the  same  point. 


B 


FIG.  73. 

Professor  Unwin 1  has  shown  that  the  maximum  unit  compression 
at  the  face  of  the  dam  occurs  on  a  section  normal  to  the  face,  and  that 
the  maximum  value  of  this  compression  at  the  outer  edge  of  a  hor- 
izontal section  through  the  dam  is  fcm  =  — ^|— ,  in  which  fc  is  the  value 

cos  (/ 

of  unit  vertical  compression  and  B  is  the  angle  made  by  the  batter  of 
the  face  of  the  dam  with  the  vertical. 

A  method  of  finding  the  maximum  diagonal  compression  and  its 
direction  at  any  point  of  a  horizontal  section  of  the  profile  of  a  dam  is 
given  by  Professor  Cain,2  which  agrees  practically  with  Unwin's 
results  for  the  stress  at  the  edge. 

Compression  upon  Inclined  Sections. — The  distribution  of  pressure 
upon  an  inclined  section  is  sometimes  investigated  and  the  maximum 
unit  stress  at  the  outer  face  of  the  dam  found  to  be  greater  than  that 

1  Proceedings,  Institution  of  Civil  Engineers,  Vol.  CLXXII,  Part  II. 

2  Transactions,  Am.  Soc.  C.  E.,  September,  1909. 


GRAVITY  DAMS 


255 


for  a  horizontal  section.  In  Fig.  74  using  the  same  profile  employed  in 
Fig.  72,  the  pressure  upon  the  inclined  section  k-n  is  that  due  to  the 
water  pressure  (H)  upon  the  inner  face  0-K  of  the  dam  combined 
with  the  weight  of  masonry  (W)  above  the  section  fc-n.  The  unit 
compression  at  n  is  obtained  in  the  same  manner  as  for  the  horizontal 
section.  This  stress  for  this  profile  is  greater  than  for  the  same  point 
when  obtained  by  using  the  horizontal  section  through  n,  and  about 
the  same  as  that  at  the  outer  edge  of  the  base  section  k-k. 

Lateral  Distribution  of  Stress. — In  the  trapezoidal  distribution 
of  stress,  which  considers  the  stresses  to  vary  uniformly  from  the  inner 
to  the  outer  edge  of  the  section, 
it  is  assumed  that  the  whole 
width  of  the  dam  acts  together  as 
a  single  homogeneous  body.  It 
is  not  probable  that  this  is  the 
case  in  a  wide  section.  The 
middle  portion  of  the  section 
carries  more  and  the  edges  less 
stress  than  the  assumed  distri- 
bution shows,  and  for  this  reason 
many  designers  have  considered 
that  the  ordinary  method,  with 
low  allowable  stress  upon  the 
outer  edge,  as  proposed  by  Ran-  FIG.  74. 

kine,  to  be  sufficiently  exact.  The 

ordinary  method,  taking  successive  horizontal  sections,  provides  an 
easy  way  of  determining  an  approximate  profile.  Careful  study 
should,  however,  be  given  to  the  possible  diagonal  stresses  in  a  high 
dam,  and  if  such  stresses  exceed  the  allowable  unit  compression,  the 
profile  should  be  widened  so  as  sufficiently  to  reduce  them. 

139.  Horizontal  Tension. — Experiments  have  been  made  by  Sir 
J.  W.  Ottley  and  Mr.  A.  W.  Brightmore 1  upon  models  of  dams  made 
of  plasticine  (a  kind  of  modeling  clay),  and  by  Messrs.  J.  W.  Wilson 
and  W.  Gore  2  on  models  made  of  india  rubber. 
The  distribution  of  stresses  through  the  profile  was  determined  in  each 
case  by  observing  the  horizontal  and  vertical  displacement  of  points 
in  the  section.  These  experiments  seemed  to  confirm,  in  general,  the 
ordinary  theory  of  the  trapezoidal  distribution  of  stresses,  and  to 
justify  the  methods  of  design  in  common  use. 

At  the  base  of  the  dam,  where  the  profile  section  joins  the  founda- 

1  Proceedings,  Institution  of  Civil  Engineers,  Vol.  CLXXII,  p.  89. 

2  Proceedings,  Institution  of  Civil  Engineers,  Vol.  CLXXII,  p.  107. 


256  MASONRY  DAMS 

tion,  it  was  found  that  a  different  distribution  of  stress  occurs,  ten- 
sion being  developed  at  the  inner  edge  of  the  base  by  the  immovability 
of  the  foundation.  Thus,  in  Fig.  75  the  shear  on  A-B,  due  to  the 
horizontal  water  pressure  causes  horizontal  or  diagonal  tension  (T) 
in  the  foundation  at  the  inner  edge  (A)  of  the  base.  In  the  plasticine 
models  diagonal  cracks  (A-C)  occurred  at  this  point  in  the 
foundation. 

Various  methods  have  been  suggested  for  meeting  or  reducing  this 
tension  by  modifying  the  shape  of  the  profile  at  the  base  or  reinforc- 
ing the  foundation.     This  does  not 
seem  necessary  for  dams  as  usually 
-b —  constructed.     A  high  masonry  dam 
is  usually  on  solid  rock  foundation, 
and  the  strength  of  the  rock  is  such 
that  no    break  in  the    foundation 
is  to  be  anticipated  from  this  cause. 
In   most    dams   the   foundation  is 


FIG  75  in  rock  at  considerable  depth  below 

the  bed  of  the  stream,  .and  the 

lower  part  of  the  dam  is  enclosed  on  both  sides  by  gravel  or  other 
soil  which  usually  may  be  considered  to  strengthen  the  dam,  although 
the  full  depth  of  water  pressure  should  be  assumed  to  act  upon  it.  If, 
however,  this  filling  is  soft  material,  which  flows  when  saturated,  it 
may  increase  the  pressure  against  the  dam  and  may  be  considered  as 
a  fluid  heavier  than  water. 

140.  Uplift. — If  a  dam  be  so  constructed  that  water  under  pres- 
sure may  penetrate  into  the  ulterior  of  the  dam  or  under  its  base,  the 
effect  of  such  pressure  must  be  considered  in  its  design.  There  is 
considerable  difference  of  opinion  among  engineers  concerning  the 
necessity  of  providing  for  uplift  in  designing  the  profiles  for  dams. 
Some  allow  for  it  in  ah1  cases;  while  others  claim  that  properly  con- 
structed masonry  or  concrete  will  be  so  nearly  water-tight  that  the 
effect  of  uplift  may  be  neglected. 

Interior  Pressure. — It  is  always  possible  that  some  water  may  be 
forced  into  imperfect  joints  in  the  masonry  and,  if  it  be  prevented  from 
escaping  at  the  lower  side  of  the  dam,  have  the  full  hydrostatic  pres- 
sure of  the  head  in  the  reservoir.  For  this  reason  it  is  important  that 
the  water  face  of  the  dam  be  made  as  nearly  impervious  as  possible, 
and  that  the  interior  of  the  dam  be  drained  so  that  any  water  passing 
into  the  masonry  may  escape  without  damage.  It  is  evident  that 
uplift  of  the  interior  of  the  masonry  can  exist  only  where  continuous 
joints  for  considerable  distances  are  filled  with  water  under  pressure. 


GRAVITY  DAMS  257 

If  concrete  be  porous  and  its  voids  filled  with  water  under  hydrostatic 
pressure,  no  uplift  occurs  until  the  pressure  becomes  sufficient  to  over- 
come the  cohesive  strength  of  the  concrete.  In  properly  constructed 
masonry  dams,  it  is  usually  unnecessary  to  consider  the  effect  of 
uplift  on  sections  above  the  base  of  the  dam. 

Upward  Pressure  on  Base. — The  probability  of  uplift  under  the 
base  of  a  dam  depends  upon  the  character  of  the  foundation.  Care- 
ful attention  should  always  be  given  to  the  determination  of  the 
character  of  the  foundation  material  to  considerable  depths  below 
the  base  of  the  dam.  The  kind  of  material  of  which  the  foundation 
is  composed,  and  the  existence  of  seams  in  the  rock,  or  of  strata  of 
permeable  material  must  be  accurately  investigated. 

When  the  foundation  is  of  solid  rock  without  seams,  if  care  be 
used  in  joining  the  base  to  the  foundation  and  cut-off  wall  be  used 
under  the  inner  edge  of  the  base,  there  is  little  chance  of  appreciable 
uplift  under  the  base. 

When  the  foundation  is  permeable  and  there  is  water  against  both 
sides,  as  is  frequently  the  case  in  dock  walls,  the  full  hydrostatic  head 
is  usually  considered  to  act  under  the  whole  base.  This  is  some- 
what excessive,  as  it  implies  that  the  dam  is  floating  upon  a  continuous 
surface  of  water.  Probably  two-thirds  of  this  pressure  would  repre- 
sent about  the  maximum  which  could  reasonably  be  expected  in  any 
case. 

When  the  foundation  is  stratified  horizontally,  so  that  water  may 
be  expected  to  pass  under  the  dam  and  escape  below,  a  uniformly  di- 
minishing upward  pressure  from  the  inner  to  the  outer  edge  of  the 
base  may  be  assumed;  the  pressure  at  the  inner  edge  being  taken 
at  about  two-thirds  the  hydrostatic  head  above  the  dam,  and  that 
at  the  lower  edge  at  zero. 

The  probability  of  upward  pressure  on  the  foundation  should 
always  be  carefully  investigated,  and  the  section,  where  necessary, 
increased  sufficiently  to  provide  weight  of  masonry  to  overcome  the 
overturning  moment  of  this  water  pressure.  This  subject  is  very 
fully  treated  in  the  discussion  of  a  paper  by  the  late  C.  L.  Harrison 
in  the  Transactions  of  the  American  Society  of  Civil  Engineers  for 
December,  1912.  Mr.  Harrison's  conclusions  are: 

1.  For  any  stable  dam,  the  uplift  in  the  foundation  cannot  act 
over  the  entire  area  of  any  horizontal  seam,  and  in  the  masonry  it 
cannot  act  over  the  entire  area  of  any  horizontal  joint. 

2.  The  intensity  of  uplift  at  the  heel  of  the  dam  can  never  be 
more,  and  is  generally  less,  than  that  due  to  the  static  head.     Also, 
this  uplift  decreases  in  intensity  from  the  heel  to  the  toe  of  the  dam, 


258  MASONRY  DAMS 

where  it  will  be  zero  if  the  water  escapes  freely,  and  will  be  that  due 
to  the  static  head  if  the  water  is  trapped. 

3.  The  uplift  in  the  foundation  should  be  minimized  by  a  cut-off 
wall,  under-drainage,  and  grouting  when  applicable;  and  in  the  dam 
itself  by  using  good  materials  and  workmanship,  and  by  drainage 
when  advisable. 

4.  The  design  should  be  based  on  the  conditions  found  to  exist 
at  each  site  after  a  thorough  investigation  by  borings,  test-pits,  and 
otherwise,  and  modified  if  found  necessary  after  bed-rock  is  uncovered. 

ART.   38.    DAMS   CURVED   IN  PLAN 

141.  Curved  Gravity  Dams. — In  constructing  dams  across  narrow 
valleys,  it  is  often  desirable  to  curve  the  dam  in  plan,  so  as  to  make  it 
form  a  horizontal  arch,  convex  upstream.  When  so  arranged,  a 
portion  of  the  water  pressure  may  be  transmitted  to  the  sides  of  the 
valley  by  arch  action,  thus  diminishing  the  overturning  moment 
which  would  exist  in  a  straight  dam  of  the  same  section. 

In  certain  locations,  the  shape  of  the  valley  and  depth  of  suitable 
foundations  make  the  use  of  the  curved  form  economical  in  saving 
materials,  although  the  length  of  dam  is  increased  by  the  curvature. 
The  curved  form  for  gravity  dams  has  not  usually  been  adopted  for 
the  purpose  of  securing  the  arch  action,  although  the  advantage  of 
the  curved  form  is  recognized  and  the  added  security  obtained  by  the 
possibility  of  the  upper  part  of  the  dam  acting  as  an  arch  is  worth 
considering  when  it  does  not  materially  increase  the  cost. 

In  order  to  develop  free  arch  action  in  any  horizontal  slice  of  a 
dam,  it  would  be  necessary  that  the  section  be  free  to  move  horizon- 
tally when  the  pressure  comes  against  it.  As  each  section  is  rigidly 
connected  with  these  above  and  below  it  and  the  base  is  attached  to 
a  practically  immovable  foundation,  the  arch  action  is  very  imper- 
fect. Near  the  top  of  a  gravity  section,  deflection  of  the  section 
may  be  sufficient  to  permit  a  portion  of  the  water  pressure  to  be 
resisted  by  the  arch,  but  in  the  lower  half  of  the  dam  such  resistance 
is  inappreciable. 

There  is  no  satisfactory  way  of  determining  how  much  of  the 
pressure  is  borne  by  the  arch  in  a  curved  gravity  dam.  In  an  analy- 
sis of  the  stresses  in  the  Cheeseman  dam,  Mr.  Silas  H.  Woodward 
estimated  1  roughly  the  amount  of  water  pressure  carried  by  the 
arch  action,  by  determining  the  deflection  at  various  points  in  the 
mid-section  of  the  dam,  considering  the  resistance  of  horizontal  slices 
1  Transactions,  Am.  Soc.  C.  E.,  Vol.  LIII,  p.  108. 


DAMS  CURVED  IN  PLAN  259 

of  the  darn  by  arch  action,  and  the  resistance  of  a  vertical  slice  as  a 
cantilever  beam,  fixed  at  the  bottom  to  the  foundation.  He  concluded 
that  in  the  Cheeseman  dam,  the  arch  carried  about  half  the  water 
pressure  at  the  top  and  about  6  per  cent  at  the  mid-height  of  the 
middle  section. 

Mr.  Woodward's  analysis  seemed  to  indicate  that,  while  added 
security  might  be  obtained  through  arch  action  at  the  top  of  the 
dam,  the  lines  of  pressure  of  the  gravity  section  were  only  slightly 
modified  by  considering  part  of  the  load  carried  by  the  arch.  His 
conclusion  was  that  no  diminution  of  the  gravity  section  would  be 
justified  because  of  dependence  upon  arch  action. 

The  use  of  curved  plans  for  gravity  dams  may  be  of  advantage 
in  affording  a  possibility  of  motion  when  expansion  and  contraction 
take  place,  without  cracking  the  masonry.  The  advantages  to  be 
gained  by  using  curved  plans,  however,  do  not  seem  sufficient  to 
make  them  worth  while  when  they  involve  increase  in  cost.  In 
constructing  gravity  dams  across  narrow  valleys  where  arch  action 
might  be  developed,  the  sides  of  the  valley  may  also  offer  considerable 
support  to  a  straight  dam,  causing  horizontal  slices  of  the  dam  to  act 
as  beams  supported  at  the  ends.  In  any  such  dam  the  actual  stresses 
are  probably  considerably  less  than  those  obtained  by  considering 
the  gravity  resistance  only. 

142.  Arch  Dams. — Dams  are  sometimes  constructed  which  depend 
for  stability  mainly  upon  arch  action,  and  are  designed  as  horizontal 
arches.  A  number  of  dams  of  this  type  have  been  constructed 
across  narrow  valleys,  with  sections  much  lighter  than  could  be  used 
for  gravity  dams.  In  some,  the  lines  of  pressure  fall  quite  outside 
the  bases  when  considered  as  gravity  sections. 

Let  A-B,  Fig.  76,  represent  a  horizontal  slice,  1  foot  thick, 
through  a  circular  dam. 

R  =  radius  of  water  face; 

t  =  thickness  of  section; 
P  =  water  pressure  per  foot  of  length; 
/c  =  unit  compression  on  the  masonry; 

h  =  height  of  water  surface  above  section; 
w  =  weight  of  water  per  cubic  foot. 

If  the  slice  be  supposed  to  act  freely  as  an  arch  and  carry  the 
water  pressure  to  the  abutments, 

_PR_whR 
*•-—'      t ®> 


260  MASONRY  DAMS 

If  a  limiting  value  of  fc  be  assumed,  the  thickness  of  section  required 
at  any  depth  will  be 

PRwhR 


For  a  dam  of  constant  radius  (R)  the  required  thickness  varies 
uniformly  with  h,  or  the  vertical  section  of  the  dam  is  triangular. 

As  the  ends  of  the  arch  at  A  and  B  are  built  into  the  sides  of  the 
valley  and  not  free  to  move  toward  the  center  0  when  subjected  to  the 
water  pressure,  the  lines  of  thrust  of  the  arch  will  not  be  exactly  axial 
as  assumed  in  Formula  (8),  and  bending  stresses  will  develop  in  the 
arch,  giving  a  maximum  compression  somewhat  greater  than  the 
average  value.  This  effect  will  usually  be  small  as  compared  with 
the  stress  due  to  arch  action,  although  French  authorities  recommend 


FIG.  76. 

that  the  line  of  thrust  be  assumed  at  the  outer  edge  of  the  middle 
third  at  the  crown,  thus  making  the  maximum  compression  double 
the  average.  The  use  of  vertical  expansion  joints  through  the 
dam,  dividing  it  into  voussoirs,  has  the  effect  of  largely  eliminating 
the  bending  stresses.  In  practice  the  bending  stress  is  commonly 
neglected,  very  conservative  values  for  fc  being  used. 

When  the  length  of  the  arch  is  small  as  compared  with  its  thick- 
ness, it  becomes  a  curved  wedge  which  acts  as  a  beam  between  the 
abutments  supporting  its  ends,  and  should  be  considered  as  a  curved 
beam — a  condition  frequently  occurring  near  the  bottom  of  a  curved 
dam,  where  the  valley  is  narrow  and  the  thickness  of  the  dam  con- 
siderable. The  thickness  obtained  by  considering  such  a  section  as 
an  arch  is  always  sufficient. 

A  masonry  structure  cannot  be  considered  to  act  as  an  arch  when 
the  thickness  of  the  arch  ring  is  more  than  from  one-quarter  to  one- 


DAMS  CURVED  IN  PLAN  261 

third  of  the  radius  of  its  outer  surface.  The  exact  limitations  within 
which  such  action  may  take  place  are  not  definitely  known  and  are 
seldom  of  importance  in  a  dam. 

Resistance  of  Vertical  Cantilever. — As  a  dam  is  rigidly  fastened  to 
the  foundation,  it  is  evident  that  complete  arch  action  cannot  take 
place,  and  that  in  the  lower  part  of  the  dam,  the  arch  can  carry  very 
little  of  the  load.  A  vertical  section  of  the  dam  may  be  considered 
as  a  cantilever  fixed  at  the  bottom  as  in  a  gravity  dam,  and  the  resist- 
ance of  the  cantilever  to  deflection  will  limit  the  extent  to  which  arch 
action  may  occur. 

Attempts  have  been  made  by  estimating  the  relative  deflections 
of  the  horizontal  arch  and  the  vertical  cantilever  at  various  heights 
upon  the  mid-section  of  the  dam,  to  determine  what  portion  of  the 
load  is  resisted  by  each.  Such  studies  have  been  made  by  Mr.  Silas 
H.  Woodward 1  for  the  Lake  Cheeseman  dam,  which  is  a  curved  dam 
of  gravity  section  (see  Section  141)  and  by  Mr.  Edgar  T.  Wheeler2 
for  the  Pathfinder  dam,  which  was  designed  as  an  arch,  and  has  a 
section  considerably  lighter  than  could  have  been  employed  in  a 
gravity  dam.  The  section  of  the  dam  has  a  width  of  10  feet  at  the 
top,  a  batter  of  .25  on  the  downstream  and  .15  on  the  upstream  face. 

These  analyses,  with  accompanying  discussions,  are  interesting 
as  throwing  light  upon  the  probable  action  of  such  dams  when  sub- 
jected to  water  pressure,  but  afford  no  means  of  determining  the 
actual  stresses  occurring.  The  vertical  cantilever  has  the  effect  of 
reducing  the  stresses  in  the  arches,  but  it  is  not  proposed  to  consider 
the  combined  actions  in  designing  dams,  or  to  attempt  to  use  the 
actual  stresses,  as  limited  by  the  cantilever  resistance  in  proportioning 
the  arches.  In  practice,  the  arches  are  given  sections  which  would 
enable  them  to  carry  the  whole  water  pressure,  and  the  vertical 
resistance  is  considered  as  a  source  of  additional  security. 

Horizontal  Shear. — As  the  dam  is  fixed  at  the  bottom  to  the  foun- 
dation and  the  various  horizontal  slices  are  not  free  to  act  independ- 
ently of  each  other,  the  thickness  at  any  point  should  be  sufficient  to 
carry  the  total  water  pressure  above  as  horizontal  shear.  If  S  be  the 
safe  unit  shear  per  square  foot,  the  thickness  should  not  be  less  than 

7  rt 

i=— — .     Such  shearing  stresses  can  exist  only  near  the  bottom  of  the 

2o 

dam,  where  it  is  rigidly  attached  to  the  foundation,  and  can  never 
reach  the  assumed  value  if  the  water  pressures  toward  the  top  of  the 
dam  are  carried  by  arch  action. 

1  Transactions,  Am.  Soc.  C.  E.,  Vol.  LIII,  p.  89. 

2  Engineering  News,  August  10,  1905. 


262  MASONRY  DAMS 

Weight  of  Masonry. — Each  horizontal  slice  of  an  arch  dam  must 
carry  the  weight  of  the  portion  of  the  dam  above  as  a  vertical  com- 
pression. This  compression  is  computed  as  in  the  gravity  section 
when  the  dam  is  empty,  and  must  not  exceed  a  safe  unit  stress 
on  any  part  of  the  section.  The  weight  of  masonry  above  also 
produces  a  distortion  of  the  horizontal  section.  The  value  of  Poisson's 
ratio  for  concrete  may  be  taken  as  approximately  one-fifth  of  the 
unit  horizontal  compression  produced  through  the  mass  of  masonry, 
if  prevented  from  expanding  laterally  is  approximately  one-fifth  of 
the  unit  vertical  compression  which  causes  it.  The  effect  of  this 
horizontal  compression  is  to  cause  an  expansion  of  the  horizontal 
section,  increasing  the  length  of  the  arch  ring,  and  deflecting  the 
crown  of  the  arch  upstream.  When  water  pressure  is  brought 
against  the  dam,  a  portion  of  the  pressure,  sufficient  to  produce  com- 
pression in  the  arch  equal  to  the  unit  horizontal  pressure  due  to  the 
vertical  load,  will  be  used  to  bring  the  arch  back  to  its  initial  position, 
and  no  deflection  due  to  arch  action  will  occur  until  this  pressure  has 
been  passed. 

When  the  crown  of  the  arch  has  been  deflected  upstream  by  the 
weight  of  masonry,  stress  is  brought  upon  the  vertical  cantilever  by 
its  resistance  to  bending  in  that  direction.  If  water  pressure  be  now 
brought  against  the  dam,  the  vertical  cantilever  action  will  offer  no 
resistance  to  downstream  motion  until  the  pressure  upon  the  arches 
becomes  sufficient  to  bring  the  dam  back  to  its  original  unloaded 
position. 

The  existence  of  this  initial  distortion  due  to  the  weight  of  masonry 
may  depend  upon  the  manner  in  which  the  dam  is  constructed.  In 
order  to  produce  this  effect  it  is  necessary  that  the  horizontal  layers  be 
completed  and  hardened  in  position  before  the  load  above  is  applied. 
If  portions  of  the  work  be  carried  up  in  vertical  sections,  or  if  vertical 
contraction  joints  be  left,  to  be  afterward  grouted,  the  deflection  due 
to  weight  of  masonry  may  take  place  only  to  a  very  limited  extent. 

Constant-angle  Arches. — Arch  dams  are  usually  constructed  across 
narrow  gorges  which  can  readily  be  spanned  by  an  arch  of  moderate 
radius.  The  gorges  vary  in  cross-section,  being  usually  much  nar- 
rower at  bottom  than  near  the  top  of  the  arch.  The  arch  at  bottom 
will  therefore  be  much  shorter  than  at  the  top  and  if  the  same  radius 
be  used  at  top  and  bottom,  or  the  centers  lie  in  the  same  vertical  line, 
the  central  angle  included  by  the  dam  will  be  greater  at  top  that  at 
bottom.  It  has  been  shown  by  Mr.  Lars  R.  Jorgensen1  that  a 
dam  with  a  constant  central  angle  of  133°  34'  requires,  theoretically, 
1  Transactions,  Am.  Soc.  C.  E.,  Vol.  LXXVIII,  p.  685. 


DAMS  CURVED  IN  PLAN  263 

the  minimum  amount  of  masonry  in  its  construction,  and  that  angles 
from  110°  to  150°  vary  but  little  from  the  minimum.  It  has  therefore 
been  proposed  to  vary  the  radius  from  the  top  to  the  bottom,  so  as  to 
keep  within  these  ranges  of  central  angles.  This  makes  the  radius 
of  the  dam  vary  with  the  width  of  the  gorge  at  different  elevations. 
Several  dams  have  been  constructed  in  which  this  principle  has  been 
approximately  applied.  The  topography  of  the  site  must  be  care- 
fully studied  in  every  instance  and  the  dam  fitted  to  its  location, 
keeping  in  mind  the  general  principles  involved. 

Temperature  Stresses. — Comparatively  little  is  known  concerning 
the  changes  of  temperature  to  be  expected  in  a  mass  of  masonry  like 
a  dam,  but  it  is  evident  that  distortions  produced  by  such  changes 
may  sometimes  be  of  importance,  and  careful  attention  should  be 
given  to  their  probable  effect.  Temperature  above  the  normal  at 
which  the  masonry  was  placed  cause  deflection  upstream  through 
expansion,  which  may  bring  bending  stresses  upon  the  vertical  section 
when  the  water  is  low  behind  the  dam.  Contractions  due  to  tem- 
peratures below  the  normal,  causing  tensile  stresses  which  the  masonry 
or  concrete  is  not  calculated  to  bear  may  cause  cracks,  or  prevent  the 
arch  action  through  shortening  the  arch  near  the  top.  It  is  desirable 
that  masonry  which  may  be  injuriously  affected  by  low  temperature, 
be  placed  when  the  temperature  is  low,  thus  giving  a  low  normal  and 
probable  small  range  below.  Mr.  Wisner 1  urges  that  reinforcement 
be  used  on  the  faces  of  the  upper  portion  of  arched  dams  to  prevent 
cracks;  vertical  rods  on  the  downstream  face  to  take  up  the  possible 
vertical  tensions  due  to  expansion,  and  horizontal  rods  on  the  up- 
stream side  to  prevent  contraction  cracks. 

143.  Multiple-Arch  Dams. — Dams  consisting  of  a  series  of  con- 
crete arches  supported  by  buttresses  are  sometimes  used  for  moderate 
heights  where  suitable  foundations  are  available  and  the  cost  of 
gravity  dams  would  be  greater.  The  amount  of  concrete  required  is 
much  less  than  for  gravity  dams,  and  where  concrete  materials  are 
expensive  considerable  savings  in  cost  may  result  from  their  use. 
The  form  work  required  and  the  thin  sections  of  concrete,  make  the 
unit  costs  much  more  than  for  gravity  dams,  and  under  favorable 
conditions  for  cheap  concrete  work  gravity  sections  may  be  cheaper 
to  construct.  As  the  buttresses  must  carry  the  thrust  of  the  water 
pressure,  it  is  essential  that  they  be  established  upon  very  substantial 
and  unyielding  foundations.  Usually  this  is  solid  rock,  although  some 
dams  of  this  type  have  been  built  upon  gravel  or  fissured  rock. 
Where  the  foundation  is  stable  but  of  character  which  may  permit 
1  Engineering  News,  August  10,  1905. 


264 


MASONRY  DAMS 


water  to  penetrate  it,  this  type  of  dam  has  advantages  over  a  gravity 
dam  on  account  of  the  less  importance  of  possible  uplift. 

Two  types  of  multiple-arch  dams  are  in  use;  (1)  those  in  which 
the  axes  of  the  arches  are  vertical,  the  water  pressures  coming  hori- 
zontally against  the  faces  and  being  transmitted  as  horizontal  thrusts 
against  the  buttresses;  (2)  those  with  inclined  axes,  the  water  pres- 
sures acting  normal  to  the  sloping  axes  and  bringing  vertical  as  well 
as  horizontal  thrusts  upon  the  buttresses. 

Let  Fig.  77  represent  an  inclined  arch  dam.  A  slice  of  the  arch 
ring  normal  to  the  axis  carries  a  water  pressure  which  varies  from 
the  crown  to  the  springing  line,  and  also  carries  a  portion  of  its  own 
weight  to  the  buttress.  If  a  slice  of  the  arch  ring  be  divided  into 
voussoirs  as  shown,  the  water  pressures  upon  each  voussoir  (Pi  —  P$) 
varies  with  the  depth  (hi-hs)  below  the  surface  of  the  water.  The 


FIG.  77. — Inclined  Multiple-Arch  Dam. 

weights  of  the  voussoirs  (Gi-Gs)  may  be  considered  as  divided  into 
components,  (N=Gcos6)  normal  to  the  section  and  (W=G  sin  6) 
parallel  to  the  section.  The  normal  components  are  carried  as  longi- 
tudinal thrusts  to  the  foundation,  while  the  parallel  components 
(Wi  —  Ws)  are  carried  by  the  arch  ring  to  the  buttress.  Having 
determined  these  loads,  an  approximate  line  of  thrust  may  be  drawn 
by  the  method  used  for  voussoir  arches  (see  Section  162),  from  which 
stresses  may  be  determined. 

In  designing  such  an  arch,  the  required  thickness  at  various  depths 
may  be  approximately  determined  by  finding  the  thickness  for  a 
horizontal  arch  at  the  same  depth,  then  using  this  thickness  in  the 
analysis,  modifying  it  as  required.  Practically  an  assumed  thickness 
is  given  the  ring  at  the  top  and  tapered  to  the  required  thickness  at 
some  point  below. 


DAMS  CURVED  IN  PLAN 


265 


When  the  arch  axis  is  vertical,  the  arch  carries  only  the  water 
pressure,  which  is  uniformly  distributed  over  the  face.  The  weight 
of  the  arch,  in  this  case,  is  normal  to  the  arch  section  and  is  carried 
vertically  to  the  foundation.  The  thickness  required  for  the  arch 
ring  may  be  found  from  Formula  (8),  (Art.  138). 

The  stresses  upon  the  buttresses  of  a  multiple-arch  dam  may  be 
found  by  the  methods  used  for  gravity  dams.  In  Fig.  78  E-F  is 
a  section  through  the  crown  of  an  inclined  arch;  A  BCD  being  the 
side  projection  of  the  buttress.  The  form  of  the  buttress  must  be 
such  that  the  resultant  thrust  upon  any  horizontal  section  A-B  will 
act  approximately  at  the  middle  of  the  section.  The  loads  acting 
are: 


H 


FIG.  78. 

(1)  The  horizontal  water  pressure  ( H  =  ^wh2L)  due  to  the  depth 
of  water  above  the  plane  A-B,  upon  a  length  of  dam  (L)  equal  to  the 
distance  between  the  middle  points  of  adjacent  arches. 

(2)  The  vertical  water  pressure  (V=  H-tan-O).    The  center  of 
pressure  for  the  vertical  water  pressure  is  at  the  center  of  gravity  of 
a  horizontal  section  of  the  water  face  of  the  arch  at  two-thirds  the 
depth  below  the  surface  of  the  water. 

(3)  The  weight  (Wi)  of  the  two  half  arches  upon  each  side  of  the 
buttress.     The  center  of  gravity  for  the  weight  of  the  arch  is  at  the 
center  of  gravity  of  the  center  line  of  a  horizontal  section  of  the 
arch  ring  which  passes  through  the  center  of  gravity  of  the  vertical 
section  (E-F)  of  the  crown  of  the  arch.     If  the  centers  of  gravity  of 
the  center  lines  of  the  arch  ring  be  determined  for  horizontal  sections 
at  the  top  and  bottom  of  the  arch,  all  intermediate  centers  will  lie 
upon  the  line  joining  these  points. 


266  MASONRY  DAMS 

(4)  The  weight  of  the  buttress  itself,  acting  through  its  center  of 
gravity. 

The  resultant  (R)  of  these  loads  should  cut  the  base  A-B  near 
its  middle  point,  in  order  to  secure  uniform  distribution  of  pressure 
over  the  section. 

Buttresses,  for  dams  of  this  type,  are  usually  made  very  thin 
in  comparison  with  their  widths,  and  are  therefore  stiffened  laterally 
by  the  use  of  horizontal  struts  from  buttress  to  buttress,  or  by  the 
use  of  cross  walls.  The  design  of  these  struts  is  purely  a  matter  of 
judgment  on  the  part  of  the  designer. 

In  the  design  of  multiple-arch  dams,  the  general  lay  out  is  a  matter 
which  must  depend  upon  local  topography.  Each  dam  is  a  problem 
by  itself,  and  must  be  made  to  fit  its  location.  It  has  been  found  that 
in  some  instances,  where  the  conditions  are  favorable  to  the  con- 
struction of  masonry  dams  of  moderate  height,  multiple-arch  dams 
may  be  built  at  much  less  cost  than  gravity  structures.  Forty  to 
60  or  70  feet  between  centers  of  buttresses  are  commonly  found 
economical  distances.  Arches  with  axes  making  angles  of  30° 
or  40°  with  the  vertical  are  apt  to  show  some  saving  of  material  as 
compared  with  vertical  axes,  but  this  is  not  always  the  case.  The  unit 
cost  of  construction  is  usually  somewhat  greater  for  inclined  arches. 

In  constructing  gravity  dams,  a  cheaper  grade  of  masonry  may  be 
employed,  and  the  form  work  costs  less  than  for  multiple-arch  dams. 
Careful  studies  of  local  conditions,  and  tentative  trial  designs  are 
necessary  in  each  case  for  best  results. 

Temperature  Stresses,  due  to  temperatures  lower  than  those  at 
which  the  arches  are  constructed,  are  to  be  expected  in  all  structures. 
These  produce  shortening  of  the  arch  and  give  tensile  stresses  which 
may  result  in  cracks  when  the  dam  is  empty.  Horizontal  reinforce- 
ment near  the  downstream  face  at  the  crown  and  near  the  upstream 
face  at  the  springing  line  is  desirable  to  resist  this  tendency  to  crack. 

ART.   39.     REINFORCED    CONCRETE  DAMS 

144.  Reinforcement  in  Arch  Dams. — Several  designers  have  used 
steel  reinforcement  in  arch  dams,  where  it  has  seemed  desirable  to 
prevent  the  possible  development  of  cracks,  or  to  give  additional 
security  where  the  uncertainty  concerning  stresses  made  tensions  seem 
possible  under  certain  conditions.  Cracks  which  may  result  from 
changes  of  temperature  when  dams  are  empty  are  frequently  guarded 
against  by  using  reinforcement,  as  has  been  mentioned  in  the  previous 
articles.  The  stresses  in  most  of  these  cases  are  practically  indeter- 


REINFORCED  CONCRETE  DAMS 


267 


minate,  and  the  reinforcement  is  placed  according  to  the  judgment 
of  the  designer. 

These  structures  are  sometimes  called  reinforced  concrete  dams  in 
published  reports,  but  are  not  designed  as  reinforced  structures  and 
are  not  properly  so  classed.  No  fully  reinforced  arch  dams  have  as 
yet  been  constructed,  and  no  dams  have  been  designed  in  which  the 
stresses  have  been  determined  by  the  use  of  the  theory  of  the  elastic 
arch. 

145.  Flat  Slab  and  Buttress  Dams. — For  dams  of  moderate 
height  reinforced  flat  slab  and  buttress  construction  has  frequently 
proven  economical.  In  this  type  of  construction  the  buttresses  are 
usually  placed  from  12  to  18  feet  apart,  and  the  slabs  extending  be- 
tween buttresses  are  inclined  at  an  angle  of  40°  to  45°  with  the  ver- 
tical so  that  the  resultant  of  the  normal  water  pressures  passes  near 
the  middle  of  the  base  of  the  buttress.  Most  of  the  dams  of  this  type 
in  use  have  been  constructed  under  the  patents  of  the  Ambursen 
Hydraulic  Construction  Company. 

Fig.  79  shows  a  dam  of  this  type  in  section  through  the  inclined 
slab.  The  loads  carried  by  the  slab  consist  of  the  normal  water  pres- 


FIG.  79. 


sure  and  the  normal  component  of  its  own  weight.  The  slab  may  be 
designed  by  the  ordinary  method  for  reinforced  concrete  beams,  but 
the  values  used  for  allowable  stresses  should  be  very  conservative. 

The  buttress  should  be  made  of  sufficient  width  to  cause  the 
resultant  thrust  upon  its  base  to  pass  approximately  through  its 
middle  point  when  fully  loaded,  and  must  have  sufficient  base  area 


268  MASONRY  DAMS 

to  keep  the  pressure  upon  the  foundation  within  reasonable  limits. 
Lateral  stiffness  of  the  buttresses  may  be  provided  by  giving  them 
sufficient  thickness,  and  using  reinforcement  on  the  sides,  or  it  may 
be  obtained  by  ties  and  struts  between  buttresses. 

In  many  dams  of  this  type,  cellular  construction  is  adopted,  in 
which  the  spaces  between  buttresses  are  divided  into  cells  by  hori- 
zontal floors,  openings  through  the  buttresses  providing  opportunity 
to  pass  under  the  dam  throughout  its  length.  Sometimes  vertical 
walls  provide  rooms  which  may  be  utilized  for  power  house  or  other 
purposes. 

Slab  and  buttress  dams,  like  any  other  masonry  dams,  require 
firm  foundations.  For  locations  where  substantial  foundations  may 
be  obtained  for  buttresses  on  porous  material,  they  possess  an  advan- 
tage over  gravity  dams  which  would  be  subjected  to  upward  pressure. 
In  these  cases  it  is  necessary  to  provide  cut-off  walls  at  the  heel  of  the 
dam  to  prevent  water  passing  under  and  washing  out  the  foundation. 

ART.  40.     CONSTRUCTION   OF  MASONRY  DAMS 

146.  Foundations. — Masonry  dams  are  ordinarily  applicable  only 
to  situations  where  foundations  of  solid  rock  may  be  obtained. 
Careful  examinations  of  the  character  of  the  rock  should  always  be 
made  to  considerable  depths  below  the  foundation  in  order  to  make 
sure  that  no  seams  or  strata  of  porous  materials  exist,  which  might 
cause  slipping  of  the  foundation  when  subjected  to  pressure  of  water 
behind  the  dam. 

Nearly  all  of  the  failures  of  masonry  dams  which  have  been 
recorded  have  been  due  to  defective  foundations,  causing  settlements 
through  washing  out  the  foundation  materials,  or  sliding  of  base  of 
dam,  and  foundation  on  seams  or  soft  strata  through  which  water 
under  pressure  found  its  way. 

Where  the  depth  to  solid  rock  is  considerable  and  the  rock  or 
gravel  near  the  surface  is  of  a  character  to  give  substantial  support 
to  the  structure,  masonry  dams  may  sometimes  be  used  without 
carrying  the  base  of  the  dam  into  the  solid  rock.  In  such  cases, 
curtain  walls  at  the  heel  of  the  dam  should  be  carried  down  to  the  rock 
to  shut  off  leakage  and  possible  washing  of  the  foundation. 

When  the  rock  is  seamed  or  fissured,  it  may  frequently  be  made 
tight  by  grouting,  which  is  done  by  drilling  into  it  and  forcing  grout 
(usually  of  neat  cement  and  water)  under  pressure  into  the  fissures 
until  the  cracks  become  sufficiently  filled  to  force  grout  to  the  surface 
through  adjacent  drill  holes. 


CONSTRUCTION  OF  MASONRY  DAMS  269 

When  a  high  dam  is  to  be  constructed,  the  geological  structure  of 
the  valley  should  be  studied,  and  core  drill  borings  made  over  the 
site  of  the  dam  so  as  to  determine  fully  the  stability  of  the  foundation 
and  the  probability  of  leakage  around  or  under  the  dam. 

The  placing  of  the  foundations  of  a  dam  is  usually  the  most  diffi- 
cult part  of  the  work  of  construction.  Commonly  it  is  necessary 
to  divert  the  water  of  the  stream  to  be  damned,  and  seepage  water 
must  be  handled  in  making  the  excavations  and  placing  the  masonry. 
The  methods  used  in  such  work  are  described  in  Mr.  Chester  W. 
Smith's  "Construction  of  Masonry  Dams,"  New  York,  1915. 

147.  Masonry  for  Dams. — Several  types  of  masonry  are  some- 
times used  in  dams  of  massive  construction. 

Heavy  rubble  masonry  has  commonly  been  employed,  in  which  the 
large  stones  are  set  in  mortar  beds,  and  the  vertical  joints  filled  with 
mortar  and  small  stones  carefully  placed  by  masons.  The  stones 
are  put  into  place  by  derricks  and  must  be  held  and  lowered  so  as 
to  seat  evenly  upon  the  mortar  bed,  being  set  with  careful  attention 
to  bond,  so  that  no  continuous  joints  exist  in  any  direction.  The 
complete  filling  of  all  joints  is  important. 

Cyclopean  masonry,  in  which  the  large  rubble  stones  are  set  in 
beds  of  concrete  and  the  joints  filled  with  soft  concrete,  has  recently 
been  used  to  considerable  extent.  The  joints  are  made  thicker 
than  mortar  joints,  and  the  labor  required  in  setting  the  stones  and 
making  good  joints  is  much  less  than  in  the  ordinary  rubble. 

Rubble  concrete  is  masonry  in  which  rubble  stones  are  distributed 
through  a  mass  of  concrete.  In  some  cases,  boulders  of  considerable 
size  are  used  in  such  work.  This  differs  from  cyclopean  masonry 
mainly  in  the  smaller  amount  of  large  stone  used  and  larger  quantity 
of  concrete.  It  uses  more  cement,  but  is  more  rapidly  constructed 
and  requires  less  hand  labor. 

Plain  concrete  is  now  frequently  used,  without  large  stone,  for 
massive  work,  as  well  as  for  the  dams  of  thin  sections.  The  plant 
required  is  less,  as  derricks  are  needed  for  handling  the  heavy  stone, 
and  usually  more  rapid  progress  is  possible  in  placing  the  concrete. 
The  nature  and  location  of  materials  and  character  of  labor  available 
determine  the  relative  costs  of  the  different  methods  of  construction. 
The  rapidity  of  construction  is  usually  greater  as  the  quantity  of 
large  stone  becomes  less. 

148.  Overflow  Dams. — When  water  is  to  flow  over  the  top  of  a 
dam  or  spillway,  the  section  must  be  modified  to  provide  for  the  pass- 
ing of  the  water  with  the  least  disturbance  possible,  and  to  take  into 
account  the  additional  head  of  water  above  the  dam. 


270  MASONRY  DAMS 

If  the  water  falls  freely  over  the  dam,  its  crest  should  be  given 
such  form  as  to  eliminate  the  possibility  of  causing  a  vacuum  behind 
the  sheet  of  falling  water.  The  effect  of  the  impact  of  the  falling 
water  must  also  be  taken  into  account,  and  provision  made  for  pro- 
tecting the  toe  of  the  dam  against  erosion,  which  is  frequently  done 
by  providing  a  water  cushion  into  which  the  stream  may  fall. 

In  overflow  weirs  of  considerable  height,  the  downstream  face  of 
the  dam  is  given  approximately  the  form  of  the  curve  that  the  water 
would  take  in  falling  freely  over  the  weir  under  maximum  head.  The 
water  may  then  follow  the  surface  of  the  dam,  and,  by  reversing  the 
curve  in  the  lower  part  of  the  section,  be  turned  to  horizontal  direc- 
tion at  the  toe  of  the  dam.  In  designing  such  a  section,  the  weight 
of  the  water  on  the  downstream  face  is  neglected,  the  pressure  on  the 
upstream  face  being  taken  as  that  due  to  the  full  head  at  greatest 
expected  flood.  Special  attention  should  also  be  given  to  the  possi- 
bility of  uplift  or  of  scouring  at  the  toe. 


CHAPTER  IX 

SLAB  AND  GIRDER  BRIDGES 
ART.   41.     LOADINGS   FOR  SHORT  BRIDGES 

149.  Highway  Bridges. — Sidewalks  of  bridges  in  towns  may  be 
considered  as  carrying  a  live  load  of  100  pounds  per  square  foot 
of  sidewalk  area.  In  the  more  crowded  districts  of  cities,  larger 
loads  are  sometimes  employed,  but  in  general  this  is  ample  for  all 
probable  occurrences. 

Roadways  of  highway  bridges  should  be  able  to  carry  the  heaviest 
motor  trucks  which  may  reasonably  be  expected  to  come  upon  them. 
In  the  development  of  truck  transportation  there  is  a  tendency  to  in- 
crease the  weights  carried  by  a  single  truck,  and  careful  attention 
should  be  given  to  this  possibility  in  designing  bridges  intended  to 
last  a  long  time.  A  motor  truck  weighing  20  tons,  with  6  tons  on  one 
axle  and  14  tons  on  the  other,  the  distance  between  wheels  being  6 
feet  and  between  axles  12  feet,  may  reasonably  be  assumed  as  a 
maximum  load  for  a  bridge  upon  an  important  country  highway  or 
street  of  a  town.  This  load  is  a  very  exceptional  one  for  ordinary 
highways  and  probably  in  most  cases  a  truck  weighing  7  to  10  tons  is 
as  large  as  is  likely  to  be  met  under  present  conditions,  and  possibly 
a  road  roller  may  be  a  more  probable  maximum  load.  The  use  of 
maximum  loads  not  likely  to  be  exceeded  in  the  near  future  is  always 
desirable  in  such  work. 

For  country  bridges  under  moderate  or  light  traffic,  a  truck  weigh- 
ing 8000  pounds  on  each  of  two  axles,  10  feet  apart,  may  be  used  as 
a  probable  maximum  load  under  present  conditions,  or  a  15-ton  road 
roller,  6  tons  on  the  front  wheel,  which  is  4  feet  wide,  and  4.5  tons  on 
each  of  the  rear  wheels,  each  20  inches  wide. 

Street  Railway  Track. — When  the  bridge  is  to  carry  a  street 
railway,  the  load  of  a  car  weighing  50  tons  on  four  axles  spaced  5,  14, 
and  5  feet  apart  may  be  assumed  as  a  probable  maximum  load.  This 
load  may  be  considered  as  distributed  over  an  area  of  bridge  floor 
about  35  feet  in  length  and  10  feet  in  width,  giving  a  maximum  uni- 
form load  of  about  300  pounds  per  square  foot. 

271 


272  SLAB  AND  GIRDER  BRIDGES 

For  light  traffic  roads,  a  car  weighing  35  tons  on  the  same  wheel 
distribution  may  be  used,  giving  a  uniform  loading  of  about  200 
pounds  per  square  foot. 

150.  Distribution  of  Concentrated  Loads. — Investigations  of  the 
distribution  of  concentrated  loads  upon  slabs  have  been  made  by 
Mr.  Goldbeck  for  the  U.  S.  Office  of  Public  Roads.  These  tests  l 
seemed  to  indicate  that  for  a  slab  whose  width  is  greater  than  its 
span,  the  effective  width  of  distribution  of  a  concentrated  load  might 
be  taken  at  about  eight-tenths  of  the  span. 

From  a  series  of  tests  at  the  University  of  Illinois,  Mr.  Slater 
concluded2  that  for  a  slab  whose  width  is  greater,  than  twice  the 
span,  the  effective  width  (e)  might  be  assumed  as  e  =  %x+d,  where 
x  is  the  distance  from  the  concentrated  load  to  the  nearest  support 
and  d  is  the  width  over  which  the  load  is  applied.  As  the  ratio  of 
width  to  span  decreases,  the  effective  width  becomes  less,  the  coeffi- 
cient in  the  formula  becoming  about  1.2  when  the  span  equals  the 
width. 

From  tests  for  the  Highway  Department  of  the  State  of  Ohio  3 
Professor  Morris  recommends  for  a  concentrated  load  applied  to  the 
concrete  floor  of  a  highway  bridge  that  e  =  Q.6S+1.7,  where  e  is  the 
effective  width  in  feet  for  a  slab  whose  width  is  greater  than  its 
span,  and  S  is  the  clear  span  in  feet.  This  agrees  well  with  the 
results  of  Mr.  Slater  if  the  load  be  placed  at  the  middle  of  the  span 
(x  =  S/2). 

When  the  load  comes  upon  the  floor  of  the  bridge  through  a  pave- 
ment or  fill,  it  may  also  be  considered  as  distributed  lengthwise  over 
a  certain  area.  For  earth  fill,  the  length  of  distribution  may  be 
taken  as  twice  the  depth  of  fill.  For  gravel  or  macadam  road  sur- 
face, three  or  four  times  the  depth  of  surface  may  be  used. 

In  T-beam  construction,  when  a  slab  is  continuous  over  several 
girders  and  a  load  comes  upon  the  slab  immediately  over  one  of  the 
girders,  the  whole  of  the  load  will  not  be  borne  by  the  girder  under 
the  load,  but  a  portion  of  it  will  be  transferred  by  the  slab  to  adjacent 
girders.  In  the  Ohio  tests  mentioned  above,  this  distribution  was 
investigated  and  the  following  conclusions  reached : 

(1)  The  percentage  of  reinforcement  has  little  or  no  effect  upon 
the  load  distribution  to  the  joists,  so  long  as  safe  loads  on  the  slab 
are  not  exceeded. 

(2)  The  amount  of  load  distributed  by  the  slab  to  other  joists  than 

1  Proceedings,  American  Society  for  Testing  Materials,  1915,  p.  858. 

2  Proceedings,  American  Society  for  Testing  Materials,  1913,  p.  874. 

3  Bulletin  No.  28,  Ohio  State  Highway  Department,  1915. 


DESIGN  OF  BEAM   BRIDGES  273 

the  one  immediately  under  the  load,  increases  with  the  thickness  of 
the   slab. 

(3)  The  outside  joists  should  be  designed  for  the  same  live  load 
as  the  intermediate  joists. 

(4)  The  axle  load  of  a  truck  may  be  considered  as  distributed 
uniformly  over  12  feet  of  roadway. 

151.  Railway  Bridges. — For  short  spans,  railway  moving  loads 
may  be  considered  as  uniformly  distributed  by  the  track  and  ballast. 
If  the  heaviest  locomotive  load  per  foot  of  length  be  distributed 
over  a  width  of  about  10  feet,  the  result  will  be  well  on  the  safe 
side.     When  the  bridge  is  covered  by  a  fill  under  the  tracks,  the 
width  of  distribution  may  be  increased  by  twice  the  depth  of  fill. 

The  weights  for  maximum  locomotive  loads  may  vary  from  about 
8000  to  10,000  pounds  per  linear  foot  of  track,  or  from  800  to  1000 
pounds  per  square  foot  when  distributed  over  a  width  of  10  feet.  For 
bridges  longer  than  about  35  feet,  it  may  be  preferable  to  use  actual 
locomotive  wheel  loads,  or  to  somewhat  reduce  the  load  per  square 
foot. 

ART.  42.  DESIGN   OF  BEAM  BRIDGES 

152.  Slab  Bridges. — When  the  span  of  a  bridge  is  not  more  than 
12  to  15  feet,  the  simple  slab  spanning  the  opening  and  resting  upon 
the  abutments  at  its  ends  is  usually  the  most  economical  form  to  use. 
Under  heavy  loading,  the  economic  limit  of  length  may  be  only  10  to 
12  feet,  while  for  lighter  loads,  slabs  16  to  20  feet  in  length  may  be 
desirable.      The   design  of  a  bridge  slab  will  be  illustrated  by  a 
numerical  example. 

Example  1. — Design  a  highway  slab  of  11  feet  clear  span,  and 
width  of  18  feet  to  carry  a  macadam  road  with  the  loading  given  in 
Section  149. 

Solution. — 

Assume  weight  of  road  material  =  80  pounds  per  square  foot. 

Weight  of  slab  =  145  pounds  per  square  foot. 


Total  dead  load  =  225  pounds  per  square  foot. 

Live  load  is  auto  truck  with  14,000  pounds  on  each  of  two  wheels 
6  feet  apart.  From  Section  150,  effective  width,  e  =  .6$-fl.7.  As 
.68  is  more  than  the  distance  apart  of  wheels,  the  loads  would  over- 
lap, and  we  consider  both  loads  distributed  over  e  =  .6£-fl.7+6  = 
14.3  feet.  The  live  load  per  foot  of  width  is  28000/14.3  =  1950 
pounds.  This  load  may  be  considered  as  applied  over  a  length  of 


274  SLAB  AND  GIRDER  BRIDGES 

1.7  feet  =  20  inches.     The  effective  length  of  the  beam  is  distance 
between  centers  of  bearings,  or  1  foot  more  than  the  clear  span. 
(11  +  1  =  12  feet.) 
Bending  moments, 

M  (live)  =  1950/2  (72-5)  =  65325  in.-lb. 

M  (impact)  =25  per  cent  of  live   =   16330  in.-lb. 

M  (dead)  =  225  X 12  X 12  X 12/8     =  48600  in.-lb. 

Total  moment,  M  =  130255  in.-lb. 

Taking  fc  =  650,  /.=  16,000,  n=15,  Table  VII  (p.  163)  gives 
#  =  108,  p  =  .0078,  j  =  .874.  12d2=  13025/108  =1206,  and  d=10 
inches. 

Maximum  shear  occurs  when  center  of  live  load  is  1.7/2  feet 
from  support,  in  which  case, 

V  (live)  =  1950X  10.65/12  =  1722  pounds. 

V  (impact)  =  25  per  cent  of  live  =  430  pounds. 
V  (dead)  =225  X 11/2  =  1238  pounds. 


Total  shear  V  =3390  pounds. 

Depth  required  for  shear, 

,     V  3390 


Make  d=10  inches,  then  allowing  concrete  to  extend  1.5  inches 
below  steel,  weight  of  beam  is  12X11.5X150/144=144  pounds  per 
square  foot,  which  is  within  the  assumed  weight. 

Reinforcement.  —  The  area  of  steel  required  per  foot  of  width, 
A  =pbd=.  0078X12X10  =  .936  in.2  From  Table  XV  (p.  199),  we 
see  that  f-inch  round  bars  spaced  5.5  inches  apart,  or  f-inch  square 
bars  5  inches  apart  will  answer.  For  the  latter  the  maximum  unit 
bond  stress  is 

V  3390  _  „     . 


Fig.  80  shows  the  slab  in  longitudinal  section.  For  lateral  rein- 
forcement J-inch  round  bars,  12  inches  apart,  are  used.  To  prevent 
cracking  due  to  negative  moment  where  the  slab  joins  the  abutments, 
^-inch  round  bars  12  inches  apart  are  placed  in  the  ends  of  the  slab 
at  the  top.  Expansion  joints,  usually  tar  paper,  are  often  placed  on 
the  top  of  the  abutment  under  the  slab,  thus  preventing  the  develop- 
ment of  negative  moment  and  allowing  for  temperature  changes. 


DESIGN  OF  BEAM   BRIDGES 


275 


153.  T-Beam  Bridges. — When  the  length  of  the  bridge  is  too  great 
for  a  simple  slab,  it  is  found  economical  to  use  girders  to  support  the 
slab.  If  the  head  room  is  sufficient  and  the  span  not  too  great,  T- 
beam  construction  may  be  used.  This  consists  of  a  series  of  T-beams 
extending  from  abutment  to  abutment,  girders  being  placed  under  the 


:&#B^^^ 


^~%square  bar5-5"c-c. 

^  Vg  round  bars-  \Z"c-c. 

m 


FIG.  80.— Slab  Bridge. 

slab  to  form  the  stems  of  the  T-beams,  and  the  slab  being  continuous 
over  the  girders  for  the  width  of  the  bridge. 

Example  2. — Design  a  T-beam  highway  bridge  with  clear  span 
of  24  feet,  to  carry  a  roadway  18  feet  wide,  using  loadings  as  in 
Example  1. 

Solution. — Allowing  12  inches  for  width  of  base  of  guard  rail, 
the  full  width  is  20  feet.  Use  five  girders,  spaced  4  feet  on  centers, 
the  outside  girders  being  2  feet  from  end  of  beam  (see  Fig.  81). 


„    -g  square  bars,  5*  c-c. 
-4,  1^  d  2. 14  round  bars. 


3LI 

— [ 

round  Stirrups 


FIG.  81.— T-beam  Girder  Highway  Bridge. 

Slab. — Weight  of  road  material  =  80  pounds  per  square  foot. 
Assume  weight  of  slab    =  100  pounds  per  square  foot. 

Total  dead  load        =  180  pounds  per  square  foot. 

The  live  load  is  a  single  wheel  load  of  14,000  pounds  distributed 
over  a  width  .6X4+1.7  =  4.1  feet.  The  live  load  per  foot  of  width 
is  14000/4.1  =  3415  pounds.  This  may  be  considered  as  distributed 


276  SLAB  AND  GIRDER  BRIDGES 

over  2  feet  of  length.  The  slab  is  continuous  and  taking  the  moment 
of  the  concentrated  load  as  four-fifths  of  the  moment  for  a  simply 
supported  beam,  we  have 

M  (live)  =  (3415/2)  (24  -  6)f  =  24588  in.-lb. 

M  (impact)  =25  per  cent  of  24588    =  6147  in.-lb. 
M  (dead)  =  180X4X4X  12/12  =  2880  in.-lb. 

Maximum  moment,  M  =33615  in.-lb. 


12  d2  =  33615/108  =  311,  and  d  =  5.1  inches. 

The  shear  is  a  maximum  when  the  load  is  placed  next  to  the 
support,  and  assuming  width  of  girder  at  12  inches, 

V.  (live)  =3415X2.5/4  =2134  pounds. 

V  (impact)  =25  per  cent  of  3415      =  533  pounds. 

V  (dead)  =  180X3/2  =   270  pounds. 


Total  shear,  V  =2937  pounds. 

and  the  depth  required  for  shear  is 
V  2967 


Using  d  =  7.0  inches, 

_  M  _         33615  _  _n  <u  •    2 
~~  16000  X.  875X7" 


From  Table  XV  (p.  199),  f-inch  square  bars  spaced  5  inches  apart 
will  answer. 

When  the  concentrated  load  is  at  the  middle  of  a  span,  adjacent 
unloaded  spans  will  be  under  negative  moment  throughout  their 
lengths.  Maximum  negative  moment  is  approximately  the  same  as 
positive  moment,  and  f-inch  square  bars  5  inches  apart  will  therefore 
be  put  through  the  top  as  well  as  the  bottom  of  the  slab. 

With  concrete  extending  1  inch  below  the  steel,  the  total  depth  of 
slab  is  8  inches  and  the  weight  of  slab  =  8X150/12  =100  pounds  per 
square  foot  as  assumed. 

Girders.  —  The  maximum  stresses  in  the  girder  occur  when  a  pair 
of  wheels  are  directly  over  the  girder.  A  portion  of  this  load  is  dis- 
tributed by  the  slab  to  adjacent  girders.  This  rolling  load  consists 
of  one  wheel  carrying  14,000  pounds  and  one  carrying  6000  pounds, 
12  feet  apart.  Assuming  this  distributed  over  a  width  of  6  feet  (see 
Section  150),  the  load  carried  by  one  girder  covers  4  feet  of  width  and 
the  loads  are  14000X4/6  =  9333  and  6000X4/6  =  4000  pounds. 


DESIGN  OF  BEAM  BRIDGES  277 

Assuming  the  stem  of  girder  to  weigh  250  pounds  per  foot,  the 
dead  load  is  180X4+250  =  970  pounds  per  linear  foot  of  girder. 

The  position  of  moving  load  for  maximum  moment  is  that  in  which 
the  heavier  wheel  is  as  far  to  one  side  of  the  middle  of  the  beam  as 
the  center  of  gravity  of  the  two  loads  is  to  the  other,  and  the  moment 
(taking  length  of  beam  as  25  feet)  is : 

M  (iiVe)  =  13333(12. 5- 1.8)2 x  12     =  732736  in.-lb. 
Zo 

M  (impact)  =25  per  cent  of  732736  =   183184  in.-lb. 
M  (dead)  =  970  X  25  X  25  X 12/8         =  909375  in.-lb. 


Total  moment,  M  =  1825295  in.-lb. 

Maximum  shear  occurs  when  the  heavier  load  is  adjacent  to  the 
support,  and  the  center  of  gravity  of  the  loads  (considering  the  loads 
distributed  over  2  feet  of  length)  is  5.1  feet  from  the  center  of  support. 

V  (live)  =  13333(25-5.1)/25  =  10133  pounds 

V  (impact)  =25  per  cent  of  10133     =  2533  pounds. 
V  (dead)  =  970  X  25/2  =  12125  pounds. 

Total  V  =24791  pounds. 

The  depth  required  for  shear  with  12-inch  width  of  stem  is 
V  24791 

1  *  £**-    lt/-L  •+    S^ 


The  girder  is  a  T-beam  with  flange  48  inches  wide  and  8  inches 
thick,  and  stem  12  inches  wide  and  20  inches  deep. 

.          ^  =  20/8  =  2.5,     and     g."  - 

From  Diagram  I  (p.  184),  we  see  that  the  neutral  axis  is  in  the  flange. 

1825295 


_ 

bd2    48X20X20 


" 


From  Table  VII  (p.  163),  we  see  that  for  /,=  16000  and  #  =  95, 
/c  =  600  and  p  =  .0068.  Then  A  =  .0068X48X20  =  6.53  inches.  From 
Table  X  (p.  166),  it  is  found  that  four  If  -and  two  IJ-inch  round  bars 
will  answer.  These  are  placed  in  two  rows,  two  1J-  and  one  1J- 
inch  bars  in  each  row,  making  the  total  depth  of  the  beam  24  inches. 
The  weight  of  stem  is  then  =16X12X150/144  =  200  pounds  per 
foot,  which  is  less  than  the  assumed  weight. 

Diagonal  Tension.  —  The  maximum  shear  at  the  middle  of  the 


278 


SLAB  AND  GIRDER  BRIDGES 


girder  occurs  when  the  moving  load  is  at  one  side  of  the  middle  of 
the  beam,  or  V  (middle)  =  9333 XI  1.5X25  =  4293  pounds;  with 

CO(\(\ 

impact  this  becomes  5366  pounds  and  v  (middle)  =  — ^~ 

LZ  X  .  o7o  X  Z(j 

=  25.5  pounds.  The  maximum  unit  shear  varies  from  25.5  lb./in.2 
at  the  middle  to  120  lb./in.2  at  the  supports.  Stirrups  are  necessary 
from  the  support  to  the  point  where  the  shear  is  40  lb./in.2  Using 
Formula  13  of  Section  108,  if  U-shaped  stirrups  of  |-inch  round 
steel  be  used,  the  spacing  at  the  ends  should  be 

2Acfs    2X.39X16000 
S=-W~:         120X12       = 

Use  this  spacing  for  eight  stirrups,  then  change  to  12  inches  spacing 
and  continue  to  middle  of  girder.  Two  of  the  horizontal  rods  may 
also  be  turned  up  near  the  abutment. 

154.  Through  Girder  Bridges. — For  spans  of  considerable  length, 
or  where  the  head  room  under  the  roadway  is  too  contracted  to  permit 


VZOW 17-0 / 

I  round  stirrupa    L6-g  square  bars 
FIG.  82.— Through  Girder  Bridge. 

the  use  of  T-beam  construction,  through  girders  may  be  used  at  the 
sides  of  the  roadway,  the  slab  floor  being  hung  from  the  bottoms  of 
the  side  girders.  The  floors  in  such  bridges  may  be  simple  slabs, 
extending  from  one  girder  to  the  other,  or  the  floor  slab  may  be 
carried  by  T-beams  across  the  bridge  from  girder  to  girder. 

Fig.  82  shows  a  bridge  of  this  type.  The  method  of  design  is  the 
same  as  for  the  other  types.  If  the  loading  of  Example  2  be  used,  the 
T-beam  cross-girder  would  carry  the  two  loads  of  14,000  pounds  each, 
6  feet  apart,  or  if  the  width  of  the  bridge  and  importance  of  traffic 
are  sufficient,  two  passing  trucks  might  give  a  loading  of  four  such 
wheels  spaced  6,  2,  and  6  feet  apart.  In  a  bridge  for  heavy  traffic, 
where  passing  loads  might  come  upon  it,  each  girder  should  be  able 
to  carry  the  whole  weight  of  a  truck  as  a  rolling  load  in  addition  to 
the  dead  weight  of  one-half  the  bridge.  On  a  country  highway,  design- 
ing for  the  passing  of  a  single  truck  is  usually  sufficient,  as  the  meeting 


DESIGN  OF  BEAM   BRIDGES  279 

of  two  unusually  heavy  loads  on  the  bridge  is  a  very  remote  contin- 
gency. 

When  sidewalks  are  to  be  carried  at  the  side  of  the  roadway,  the 
through  girder  may  be  placed  between  the  roadway  and  sidewalk,  and 
the  sidewalk  carried  by  cantilever  beams  attached  to  the  girders. 
These  cantilevers  should  be  continuations  of  the  cross-girders,  the 
tension  steel  extending  through  the  main  girder  and  being  anchored 
into  the  cross-girders. 

Example  3.  —  Design  the  principal  members  for  a  bridge  of  35  feet 
clear  span,  17  feet  wide  between  girders,  to  carry  roadway  and  loads 
as  in  Example  2.  Also  to  carry  sidewalks  5  feet  wide,  loaded  with 
100  pounds  per  square  foot. 

Solution.  —  Assume  the  spacing  of  cross-girders  at  4  feet  c.  to  c. 
and  the  road  slab  as  in  Example  2;  slab  8  inches  thick,  d  =  7  inches, 
f-inch  square  steel  5  inches  c.  to  c.  top  and  bottom. 

Cross-beams.  —  The  dead  load  upon  the  T-beams,  assuming  weight 
of  stem  at  150  pounds  per  linear  foot  will  be  180  X4+  150  =  870  pounds 
per  linear  foot.  The  live  load  is  composed  of  two  14,000  pounds 
wheel  loads,  6  feet  apart.  As  these  are  distributed  over  6  feet  of 
width,  14000X4/6  =  9333  will  be  carried  by  the  4  feet  width  of  beam. 

The  effective  length  of  beam  is  18  feet,  and 


lo 

M  (impact)  =25  per  cent  of  700000  =     175000  in.-lb. 

•MTU     j\     870X18X18X12 

M  (dead)  =  -  =    422820  m.-lb. 

o  _ 

Total  moment,  M  =  1297820  in.-lb. 

Assuming  that  the  nearest  wheel  load  may  pass  18  inches  from 
the  side  girder,  maximum  shear  in  the  cross-beam  is 

T7  ,..     ,      18666(18-5) 

V  (live)  =  -  =  13480  pounds. 

lo 

V  (impact)  =25  per  cent          =  3370  pounds. 
V  (dead)  =870X9  =  7830  pounds. 

Total  shear,  V  =24680  pounds. 

Assuming  width  of  stem  of  T-beam  to  be  12  inches,  we  have  the 
required  depth, 

V  24680 


280  SLAB  AND  GIRDER  BRIDGES 

By  Table  VII  (p.  163),  for  fs  =  16000  and 

1297820 
48X19.5X19.5 

we  find  fc  =  500  and  p  =  .005.     Then 

A=p6d=.005X48Xl9.5=4.68in.2 

Use  six  f -inch  square  bars,  four  in  lower  row,  two  in  upper. 

The  total  depth  of  beam  is  22  inches,  and  the  weight  of  the  stem 
is  12X14X150/144=175  pounds  per  linear  foot,  25  pounds  more 
than  assumed. 

Using  U-shaped  stirrups  of  J-inch  round  bars,  the  spacing  at  end 
of  beam  is 

2X. 39X16000 


120X12 


=  9  inches. 


Place  eight  stirrups  with  this  spacing  then  space  12  inches  apart 
to  middle  of  span. 

The  sidewalk  slab  carries  100  pounds  per  square  foot  moving 
load,  on  4-foot  continuous  spans.  We  will  make  it  3  inches  thick, 
reinforced  with  f-inch  round  bars  6  inches  apart.  The  sidewalk 
supports  are  cantilever  beams  carrying  4  feet  of  sidewalk  with  its 
load  and  4  feet  of  handrail  at  the  end. 

Side  Girders. — The  sidewalk  with  its  load  weighs  about  800 
pounds  per  foot  of  girder.  One-half  the  weight  of  bridge  floor  and 
T-beams  is  1900  pounds  per  foot.  Assume  weight  of  girder  as  1600 
pounds  per  foot,  and  the  total  dead  load  is  4300  pounds  per  linear 
foot. 

The  maximum  moving  load  is  the  weight  of  a  truck  whose  nearest 
wheels  are  18  inches  from  the  girder.  These  loads  are 

28000X(18-5)  =  202()0  and  12000X(18-5)=87()olb>  12  fe 

lo  lo 

Take  effective  length  of  girder  as  36  feet  and  we  have 

M  (live)  =289°°(1J*~1-8)2X  12  =  2528200  in.-lb. 

ob 

M  (impact)  -25  per  cent  of  2528200         =     632050  in.-lb. 
M  (dead)  =4300XQ36X36X  12  =  8359200  in.-lb. 


Total  M  =11519450  in.-lb. 


T    70          J-J-OlcMOU          -tnnnnr* 

bd2=  — r —  =  106666. 


DESIGN  OF  BEAM   BRIDGES  281 

Assuming  6  =  20  inches,  we  find  d  =  73  inches. 


Table  X  shows  that  nine  If  -inch  square  bars  may  be  used,  or  six 
If  -inch  square  bars  will  answer.  These  can  be  spaced  four  in  the 
lower  and  two  in  upper  row.  The  maximum  bond  stress  for  the 
latter  is 

V  106250  „    .. 


Shear.  —  Considering  the  live  loads  to  be  applied  over  a  length 
of  2  feet, 

V  (live)  =  28900(36  -  5.  1)  /36  =  24800  pounds. 

V  (impact)  =25  per  cent  of  24800      =     6200  pounds. 
7  (dead)  =4300X17.5  =  75250  pounds. 


Total  7  =  106250  pounds. 

The  maximum  shear  at  the  middle  of  the  beam  occurs  when  the 
heavier  load  is  just  past  the  middle  point,  or 

7  =  28900(18-4. 6)/36  =  10760  pounds, 
and 

10760  n  „    ..    2 

=  9  lb./in.2 


20  X. 875X73 

The  maximum  shear  varies  from  83  lb./in.2  at  the  support  to  9  lb./in.2 
at  the  middle  of  the  girder.  Reinforcement  for  diagonal  tension 
is  needed  where  v  is  more  than  40  lb./in.2  If  U-shaped  stirrups 
be  spaced  12  inches  apart,  at  the  abutment, 

_6t«_20X83X12  .    2 

~2fs~  2X16000   " 

By  Table  X,  f-inch  round  bars  are  needed.  The  tops  of  these  bars 
should  be  turned  into  hooks  to  secure  ample  bond.  Seven  stirrups 
will  be  used  spaced  12  inches  apart,  three  spaced  18  inches  and 
two  spaced  30  inches,  at  each  end  of  the  girder. 

Hangers. — To  prevent  the  T-beams  breaking  loose  from  the 
girders,  bars  passing  under  the  steel  in  the  stem  of  the  T-beam,  and 
extending  up  into  the  girder  are  used  to  carry  the  reactions  at  the 
ends  of  the  T-beams.  These  reactions  equal  the  maximum  shear 
upon  the  T-beams,  and  the  area  of  steel  required  is  Ah  =  24245/16000 
=  1.52  in.2  By  Table  X,  we  find  1-inch  round  bars  to  be  needed. 
These  should  extend  upward  a  distance  sufficient  to  develop  a. bond 
strength  equal  to  the  tensile  strength  of  the  bars,  or  at  least  50 
diameters. 


CHAPTER  X 
MASONRY  ARCHES 

ART.  43.    VOUSSOIR  ARCHES 

155.  Definitions. — A  masonry  arch  is  a  structure  of  masonry 
spanning  an  opening  and  carrying  its  loads  as  longitudinal  thrust, 
which  exert  outward  as  well  as  vertical  thrusts  upon  the  abutments. 
A  voussoir  arch  is  one  in  which  the  arch  ring  is  composed  of  a  number 
of  independent  blocks  of  stone  or  masonry. 

Parts  of  an  Arch. — The  principal  parts  of  an  arch  are  as  follows : 


FIG.  83. 

The  under  or  concave  surface  of  an  arch  is  called  the  soffit.    The  outer 
or  convex  surface  is  the  back. 

The  crown  is  the  highest  part  of  the  arch  ring  (E-F,  Fig.  82). 

The  skewbacks  are  the  joints  at  the  ends  of  the  arch  where  it 
rests  upon  the  abutments  (C-A,  B-D,  Fig.  83). 

The  intrados  is  the  intersection  of  the  soffit  with  a  vertical  plane 
perpendicular  to  the  axis  of  the  arch  (A-E-B,  Fig.  83). 

The  extrados  is  the  intersection  of  the  outer  surface  with  a  vertical 
plane  perpendicular  to  the  axis  (C-F-D,  Fig.  83). 

The  springing  lines  are  the  intersections  of  the  skewbacks  with 
the  soffit. 

282 


VOUSSOIR  ARCHES  283 

The  span  is  the  distance  between  springing  lines. 

The  rise  is  the  perpendicular  distance  from  the  highest  point  of 
the  intrados  to  the  plane  of  the  springing  lines. 

The  voussoirs  are  the  wedge-shaped  stones  of  which  an  arch  is 
composed. 

The  keystone  is  the  voussoir  at  the  crown  of  the  arch  (E-F) . 

The  springers  are  the  voussoirs  next  the  skewbacks. 

The  haunch  is  the  portion  of  the  arch  between  the  keystone  and 
springers. 

The  arch  ring  is  the  whole  set  of  voussoirs  from  skewback  to  skew- 
back. 

The  ring  stones  are  voussoirs  showing  on  the  face  of  the  arch. 

The  arch  sheeting  is  the  portion  of  the  arch  ring  not  showing  at  the 
ends. 

Backing  is  masonry  above  and  outside  the  arch  ring. 

The  spandrel  is  the  space  between  the  back  of  the  arch  and  the 
roadway  above.  The  walls  above  the  ring  stones  at  the  ends  of  the 
arch  are  spandrel  walls  and  the  filling  between  these  walls  is  spandrel 
filling. 

Kinds  of  Arches. — A  full-centered  arch  is  one  whose  intrados  is  a 
semicircle.  A  segmental  arch  is  a  circular  arch  whose  intrados  is  less 
than  a  semicircle.  A  pointed  arch  has  an  intrados  composed  of  two  cir- 
cular arcs  which  intersect  at  the  crown.  A  three-centered  arch  com- 
posed of  arcs  tangent  to  each  other  is  sometimes  called  a  basket- 
handled  arch. 

A  right  arch  is  one  whose  ends  are  perpendicular  to  its  axis.  An 
arch  whose  ends  are  oblique  to  its  axis  is  called  a  skew  arch. 

Hinged  arches  are  those  in  which  hinged  joints  are  used  at  crown 
and  skewback.  Those  without  hinges  are  called  solid  arches. 

156.  Theory  of  Stability. — A  voussoir  arch  is  supposed  to  be 
composed  of  a  number  of  independent  blocks 
in  contact  with  each  other  and  held  in  place  |W 

by  the  pressures  between  them.  In  Fig.  84, 
let  A  BCD  represent  a  voussoir  at  any  part  of 
an  arch  ring.  If  P  is  the  pressure  received  from 
the  voussoir  above  and  W  the  external  load 
carried  by  the  voussoir,  the  resultant,  R,  of  _ 

these  forces  will  be  the  pressure  transmitted  to 

the  voussoir  below.  If  the  line  of  action  of  this  resultant  should 
pass  outside  of  the  joint  A-D,  the  arch  will  fail  by  the  voussoir 
rotating  about  the  edge  of  the  joint. 

If  the  point  of  application  of  R  is  outside  the  middle  third  of 


284  MASONRY  ARCHES 

A-D,  there  will  be  a  tendency  for  the  joint  to  open  on  the  opposite 
side,  and  the  area  of  contact  between  the  voussoirs  will  be  reduced. 
If  the  line  of  action  of  R  makes  an  angle  with  the  normal  to  the  joint 
A-D  greater  than  the  angle  of  friction  for  the  surfaces  upon  each 
other,  the  voussoirs  may  slide  upon  each  other,  causing  failure  of  the 
arch. 

For  stability  of  the  arch: 

(1)  The  resultant  pressures  between  voussoirs  should  act  within 
the  middle  third  of  the  joints. 

(2)  The   components  of  the  resultant  pressures  parallel  to  the 
joints  (R  sin  a)  should  be  less  than  the  frictional  resistance  of  the 
voussoirs  to  sliding  upon  each  other. 

(3)  The  unit  pressures  at  the  surfaces  of  contact  should  be  less 
than  the  safe  compressive  strength  of  the  material  of  the  voussoirs. 

If  6  represents  the  width  of  the  joint  AD,  x  the  distance  of  the 
point  of  application  of  R  from  the  nearest  edge  and  a  the  angle  made 
by  R  with  the  normal  to  the  joint,  the  maximum  unit  compression 
will  be  represented  by 


fe  =  ws  a.     (See  Section  126.) 

Usually  the  angle  a  is  so  small  that  cos  a.  may  be  taken  as  1  with- 
out sensible  error,  or  R  may  be  considered  as  equal  to  its  normal  com- 
ponent. 

Line  of  Pressure.  —  If  an  arch  ring  be  divided  into  a  number  of 
voussoirs,  and  the  points  of  application  of  the  resultant  pressures 
upon  the  joints  between  these  voussoirs  be  determined,  the  broken 
or  curved  line  joining  these  points  of  application  is  known  as  the  line 
of  pressure  for  the  arch.  In  Fig.  85  the  line  abcdef  is  called  the  line  of 
pressure  for  the  half  arch,  when  H  is  the  crown  thrust  and  PI,  Pz,  etc., 
are  the  external  loads  coming  upon  the  several  divisions.  The  true 
line  of  pressure,  or  of  resistance,  is  a  curve  circumscribing  the  poly- 
gon abcdef.  The  larger  the  number  of  divisions  of  the  arch  ring,  the 
more  nearly  will  the  polygon  approach  this  curve. 

In  determining  the  line  of  pressure,  the  arch  ring  is  divided  into  a 
convenient  number  of  parts,  usually  six  to  sixteen  on  each  side  of  the 
crown,  and  the  external  loads  (pi-ps,  Fig.  85)  coming  upon  the  vari- 
ous divisions  are  found.  It  is  now  necessary  to  know  certain  points 
through  which  the  line  of  pressure  must  pass  in  order  to  draw  it.  If 
the  arch  be  hinged,  the  line  of  pressure  must  pass  through  the  centers 
of  the  hinges  and  may  be  drawn  without  difficulty.  In  a  solid  arch, 
the  points  of  application  of  the  pressures  upon  the  various  joints  are 


VOUSSOIR  ARCHES 


285 


not  definitely  known,  and  certain  assumptions  must  be  made  concern- 
ing them.  Any  number  of  different  lines  may  be  drawn  as  these 
assumptions  are  varied. 

Hypotheses  for  Line  of  Pressure. — If  Fig.  85  represent  half  of  a 
symmetrically  loaded  arch,  the  crown  pressure  H  will  be  horizontal. 
Assuming  its  point  of  application,  a,  and  that  its  line  of  resistance 
passes  through  a  definite  point  on  one  of  the  other  joints  as  /,  the 
amount  of  H  may  be  found  by  taking  a  center  of  moments  at  /  and 
writing  the  moment  equation  for  aU  the  loads  upon  the  half  arch 
equal  to  zero.  H  is  then  known  in  amount,  direction  and  point  of 
application  and  the  line  of  pressure  may  be  drawn,  as  shown. 

Several  hypotheses  have  been  proposed  for  the  purpose  of  fixing 
the  position  of  the  line  of  thrust.  Professor  Durand-Claye  assumed 


FIG.  85. 

that  the  true  line  of  resistance  is  that  which  gives  the  smallest  abso- 
lute pressure  upon  any  joint.  This  method  is  outlined  in  Van 
Nostrand's  Engineering  Magazine,  Vol.  XV,  p.  33.  Professor 
Winkler  suggested  that  "for  an  arch  ring  of  constant  cross-section, 
that  line  of  resistance  is  approximately  the  true  one  which  lies  nearest 
to  the  axis  of  the  arch  ring,  as  determined  by  the  method  of  least 
squares."  No  practicable  method  of  applying  this  principle  to  ordi- 
nary cases  of  voussoir  arches  has  been  devised.  Moseley's  hypothesis 
was  that  the  true -line  of  resistance  is  that  for  which  the  thrust  at  the 
crown  is  the  least  consistent  with  stability.  This  occurs  (Fig.  85) 
when  H  is  at  the  highest  and  R  at  the  lowest  point  it  can  occupy  on 
the  joint.  This  hypothesis  is  the  basis  of  Scheffler's  method  of 
drawing  the  line  of  resistance. 

Scheffler's  theory  assumes  that  H  is  applied  at  the  upper  edge  of 
the  middle  third  of  the  crown  joint,  and  that  the  value  of  H  is  such  as 


286  MASONRY  ARCHES 

to  cause  the  line  of  pressure  to  touch  the  lower  edge  of  the  middle 
third  at  one  of  the  joints  (as  d,  e,  or  /)  nearer  the  abutment.  The 
joint  at  which  the  line  of  pressure  is  tangent  to  the  lower  edge  of  the 
middle  third  is  known  as  the  joint  of  rupture.  The  joint  of  rupture 
may  be  found  by  taking  moments  about  the  lower  edge  of  the  middle 
third  of  each  of  several  joints  and  solving  for  H.  All  loads  acting 
between  the  joint  considered  and  the  crown  should  be  used  in  obtain- 
ing the  moment,  and  the  one  giving  the  largest  value  of  H  is  the  joint 
of  rupture.  The  value  of  H  so  determined  is  the  least  consistent 
with  stability,  as  a  less  value  causes  the  line  of  pressure  to  pass  out- 
side the  middle  third  at  the  joint  of  rupture. 

Should  it  be  found  that  the  line  of  pressure  passes  outside  the 
middle  third  on  the  upper  side  of  any  of  the  joints  between  the  joint 
of  rupture  and  the  crown,  the  point  of  application  of  H  may  be 
lowered  without  violating  the  hypothesis.  This  leads  to  the  usual 
statement  that  "if  any  line  of  pressure  can  be  drawn  within  the  middle 
third  of  the  arch  ring  the  arch  will  be  stable."  This  is  justified  by 
common  experience. 

When  the  loading  upon  the  arch  is  not  symmetrical,  this  method 
of  finding  the  crown  thrust  cannot  be  used,  and  in  this  case  it  is  usual 
to  select  three  points  through  which  to  pass  the  line  of  pressure, 
one  at  the  crown  and  one  near  each  abutment.  A  line  of  pressure  is 
then  passed  through  these  three  points,  and  if  the  line  so  found  does 
not  remain  within  the  middle  third  of  the  arch  ring  the  positions  of 
the  points  may  be  changed  and  new  lines  constructed.  This  may 
be  repeated  until  it  is  determined  whether  any  line  of  pressure  can 
be  drawn  within  the  middle  third. 

ART.  44.  LOADS  FOR  MASONRY  ARCHES 

157.  Live  Loads  for  Highway  Bridges. — For  the  floors  of  open 
spandrel  arch  bridges,  live  loads  should  be  considered  in  the  same 
manner  as  for  slab  bridges  (see  Art.  41).  In  investigations  of  arch 
rings,  live  loads  are  usually  taken  as  uniformly  distributed.  The 
loading  which  should  be  used  in  any  design  depends  upon  the  location 
of  the  bridge,  the  character  of  traffic,  and  the  length  of  span. 

A  heavy  (20-ton)  motor  truck  may  bring  a  load  of  about  140 
pounds  per  square  foot  upon  a  bridge  of  short  span  (about  40  feet). 
Bridges  60  to  100  feet  span  subjected  to  traffic  of  motor  trucks  and 
heavily  loaded  wagons  may  be  considered  to  carry  about  100  pounds 
per  square  foot.  For  longer  bridges  this  load  may  be  lessened,  bridges 
over  200  feet  being  designed  for  about  75  pounds  per  square  foot. 


LOADS  FOR  MASONRY  ARCHES  287 

For  bridges  less  than  100  feet  in  length  carrying  street  railways, 
a  load  of  1800  pounds  per  foot  of  length  for  each  track  may  be  taken. 
For  spans  of  200  feet  or  more,  this  may  be  reduced  to  1200  pounds  per 
foot  of  track.  These  loads  are  considered  as  distributed  over  a 
width  of  about  9  feet,  giving  loads  of  200  and  133  pounds  per  square 
foot  respectively.  For  spans  between  100  and  200  feet,  the  loads  may 
vary  according  to  the  length  of  span. 

For  light  traffic  lines  on  country  roads,  a  load  of  1200  pounds  per 
foot  of  track  may  be  used  for  arches  less  than  100  feet  in  length  and 
1000  pounds  per  foot  for  those  200  feet  or  more  in  length.  Fre- 
quently bridges  must  be  built  for  special  service,  or  where  the  traffic 
conditions  are  unusual  and  should  be  designed  for  any  loads  that  may 
reasonably  be  expected  to  come  upon  them.  Traffic  conditions  are 
constantly  undergoing  important  changes,  and  in  determining  the 
loading  to  be  used  in  any  particular  instance,  it  is  desirable  to  con- 
sider the  possible  effect  upon  future  traffic  of  the  rapid  increase  in 
the  use  of  heavy  auto-trucks  and  traction  engines.  As  masonry 
arches  are  structures  of  permanent  character,  the  probable  future 
development  of  traffic  should  be  considered  and  liberal  loadings  used 
in  design. 

158.  Live  Loads  for  Railway  Arches. — Standard  locomotive  load- 
ings are  used  in  the  design  of  floor  systems  for  open  spandrel  arches, 
as  in  beam  bridges,  and  are  also  sometimes  employed  in  investiga- 
tions of   arch   rings.     Equivalent  uniform  loadings  may,  however, 
commonly  be  used  in  arch-ring  design. 

Loadings  should  correspond  with  the  heaviest  locomotive  and 
train  loads  to  be  expected.  For  spans  less  than  about  60  feet,  a  load 
of  8000  pounds  per  foot  of  track,  or  1000  pounds  per  square  foot  of 
road  surface  is  frequently  used.  When  the  span  is  80  feet  or  more 
a  load  of  5600  pounds  per  foot  of  track,  or  about  700  pounds  per 
square  foot,  is  used,  which  are  approximately  the  same  as  Cooper's 
E  40  loading.  Impact  is  not  taken  into  account  in  the  arch-ring 
investigation. 

A  concentrated  load  upon  a  fill  may  be  considered  as  distributed 
downward  through  the  fill  at  an  angle  of  45°  with  the  vertical,  the 
top  of  the  distributing  slope  being  taken  from  the  ends  of  the  ties. 
Wheel  loads  are  taken  as  distributed  over  three  ties  and  then  trans- 
mitted to  the  filling. 

159.  Dead  Loads. — In  arch  bridges,  the  dead  weights  of  the  arch 
ring  and  of  the  filling  or  structure  above  constitute  the  principal 
loads  upon  the  arch  rings.     The  live  loads  are  much  less  in  amount, 
and  are  important  mainly  as  producing  unsymmetrical  loading  when 


288  MASONRY  ARCHES 

the  load  does  not  extend  over  the  whole  arch.  In  computing  the  dead 
load  upon  an  arch  ring,  the  actual  weights  of  the  materials  to  be 
used  should  be  taken  when  they  are  accurately  known.  It  is  common 
to  assume  the  weight  of  earth  filling  as  100  pounds  per  cubic  foot,  and 
that  of  concrete  of  other  masonry  as  150  pounds  per  cubic  foot. 

In  open-spandrel  arches  the  dead  weights  act  vertically  through 
the  columns  or  walls  supporting  the  floor  of  the  roadway,  and  may  be 
readily  computed.  When  the  spandrels  are  filled  with  earth,  each 
section  of  the  arch  ring  is  assumed  to  carry  the  weight  of  the  filling 
and  roadway  vertically  above  it. 

The  earth  pressures  upon  the  inclined  back  of  the  arch  ring 
are  not  actually  vertical,  but  may  have  certain  horizontal  com- 
ponents. For  arches  of  small  rise,  these  horizontal  pressures  are 
small  and  may  be  neglected,  but  when  the  rise  of  the  arch  is  large, 
the  horizontal  earth  thrusts  may  be  considerable,  and  should  be  taken 
into  account,  although  their  omission  is  usually  an  error  on  the  safe 
side.  While  the  amount  of  horizontal  earth  pressure  cannot  be  exactly 
determined,  it  is  usual  to  use  Rankine's  minimum  value  for  unit 
horizontal  earth  pressure  in  terms  of  the  unit  vertical  pressure, 
which  is 

rr  1  — sin  6 


in  which  H  is  the  horizontal  and  V  the  vertical  unit  pressure,  and 
0  the  angle  of  friction  for  the  earth.  For  ordinary  earth  filling,  this 
would  make  the  unit  horizontal  pressure  at  any  point  approximately 
one-fourth  of  the  unit  vertical  pressure  at  the  same  point,  the  prob- 
ability being  that  a  horizontal  pressure  of  at  least  this  amount  may 
always  be  developed. 

The  methods  used  for  determining  pressures  upon  retaining  walls 
evidently  are  not  applicable  to  this  case.  The  actual  horizontal 
earth  pressure  may  vary  within  rather  wide  limits,  and  cannot  be 
accurately  determined.  In  retaining-wall  design,  the  maximum 
earth  thrust  which  may  come  against  the  wall  is  computed,  while 
for  the  arch  we  need  to  know  the  minimum  horizontal  pressure  which 
may  be  relied  upon  to  help  sustain  the  arch.  That  the  actual  pres- 
sure may  sometimes  be  considerably  more  than  the  computed  mini- 
mum is  quite  probable. 

When  an  arch  carries  a  continuous  masonry  wall,  as  in  an  opening 
through  the  wall  of  a  building,  or  the  spandrel  wall  at  the  end  of  an 
arch  bridge,  the  wall  itself  would  arch  over  the  opening  and  be  cap- 
able of  self-support  if  the  arch  were  removed.  The  load  upon  the 


DESIGN  OF  VOUSSOIR  ARCHES  289 

arch  would  therefore  be  only  that  due  to  a  triangular  piece  of  wall 
immediately  above  the  arch  as  in  the  case  of  a  stone  lintel.  (See 
Section  53.) 

ART.   45.     DESIGN   OF   VOUSSOIR  ARCHES 

160.  Methods  of  Design. — In  designing  masonry  arches,  the  form 
and  dimensions  of  the  arch  ring  are  first  assumed  and  the  stability 
of  the  arch,  as  assumed,  is  then  investigated.     The  graphical  method 
of  investigation  is  commonly  employed,  a  line  of  pressure  (see  Sec- 
tion 156)  being  drawn  and  the  maximum  unit  compression  computed. 
Stability  requires  that  the  line  of  pressure  remain  within  the  middle 
third  of  the  arch  ring  and  that  the  unit  compression  does  not  exceed 
a  safe  value.     If  the  first  assumptions  are  not  satisfactory  the  shape 
or  dimensions  of  the  arch  ring  may  be  modified  and  the  new  assump- 
tions tested  as  before. 

Arches  subjected  to  the  action  of  moving  loads  should  be  tested 
for  conditions  of  partial  loading,  which  may  cause  unsymmetrical 
distortion  of  arch  ring,  as  well  as  for  full  load  over  the  whole  arch. 
For  ordinary  loadings  and  spans  of  moderate  length,  it  is  usually  suffi- 
cient to  draw  the  line  of  pressure  for  arch  fully  loaded  and  with  live 
load  extending  over  half  the  arch,  but  in  large  and  important  struc- 
tures, or  those  with  unusual  loadings,  it  may  be  desirable  to  test 
the  arch  ring  with  live  loads  in  other  positions  which  seem  likely  to 
produce  maximum  distortions  of  the  line  of  pressure. 

161.  Thickness  of  Arch  Masonry. — The  choice  of  dimensions  for 
the  trial  arch  ring  is  necessarily  based  upon  judgment  founded  upon 
knowledge  of  the  dimensions  of  existing  arches,  which  are  found  to 
differ  widely,  and  rules  have  been  formulated  by  several  authorities 
for  the  purpose  of  aiding  in  selecting  the  dimensions. 

Crown  Thickness. — Several  different  formulas  have  been  proposed 
for  determining  the  thickness  at  the  crown.  Trautwine's  formula 
for  the  depth  of  keystone  of  first-class  cut-stone  arches,  whether 
circular  or  elliptical,  is 

.     ,          VRadius+half  span         „ 
Depth  of  key  in  feet  =  —  — j—  -+.2  foot. 

For  second-class  work  this  depth  may  be  increased  about  one- 
eighth  part;  or  for  brick  or  rubble  about  one-third. 

Rankine's  formula  for  the  depth  of  keystone  for  a  single  arch  is 


Depth  in  feet  =  v.  12  radius. 


290 


MASONRY  ARCHES 


This  gives  results  which  agree  fairly  well  with  Trautwine's 
formula.  For  an  arch  of  a  series,  Rankine  also  recommends 

Depth  in  feet  =  V.17  radius. 

These  formulas  make  the  thickness  depend  upon  the  span  and 
rise  of  the  arch  without  regard  to  the  loading.  They  agree  fairly 
well  with  many  examples  of  existing  arches,  but  make  the  thickness 
rather  large  for  arches  of  moderate  span. 

Douglas  Formulas. — In  Merriman's  American  Civil  Engineer's 
Pocket  Book,  Mr.  Walter  J.  Douglas  gives  the  following  rules  for 
thickness  at  crown: 

THICKNESS  IN  FEET  AT  CROWN  FOR  HIGHWAY  ARCHES 


Kind  of  Masonry. 

SPAN  IN  FEET=L. 

Under  20. 

20  to  50. 

50  to  150. 

Over  150. 

First-class  ashlar.  .  .  . 
Second-class  ashlar 
or  brick  
Plain  concrete  
Reinforced  concrete.  . 

0.04(6+L) 

0.06(6+L) 
0.04(6+L) 
0.03(6+L) 

0.  020(30  +L) 

0.  025(30  +L) 
0.020V30+L) 
0.  015(30  +L) 

0.  00012(11000  +L2) 

0.00016(1  1000  +L2) 
0.00014(11000+7,2) 
0.00010(1  1000  +L2) 

0.018(75+L) 

0.  025(75  +L) 
0.  020(75  +L) 
0.  016(75  +L) 

For  railroad  arches,  add  25  per  cent  for  arches  20-  to  50-feet  span,  20  per  cent  for  50  to  150 
feet,  and  15  per  cent  for  those  over  150  feet. 

These  formulas  give  smaller  thickness  for  highway  arches  of  short 
span  than  Trautwine's  and  do  not  vary  the  thickness  with  the  rise  of 
the  arch. 

Thickness  at  Skewback. — If  the  arch  ring  be  made  of  uniform  thick- 
ness, the  unit  pressure  at  the  ends  will  be  greater  than  at  the  crown. 
The  pressure  may  often  be  made  fairly  uniform  by  making  the  thick- 
ness at  any  radial  joint  equal  to  the  crown  thickness  times  the  secant 
of  the  angle  made  by  the  joint  with  the  vertical. 

In  the  American  Civil  Engineer's  Pocket  Book,  Mr.  Douglas 
recommends  that  the  thickness  at  the  springing  line  of  a  masonry 
arch  be  obtained  by  adding  the  following  percentages  to  the  crown 
thickness : 

(1)  Add  50  per  cent  for  circular,  parabolic,  and  catenarian  arches 
having  a  ratio  of  rise  to  span  less  than  one-quarter. 

(2)  Add  100  per  cent  for  circular,  parabolic,  catenarian,  and  three- 
centered  arches  having  a  ratio  of  rise  to  span  greater  than  one-quarter. 

(3)  Add   150  per  cent  for  elliptical,   five-centered  and   seven- 
centered  arches. 

Mr.  Douglas  recommends  that  the  top  thickness  of  abutments 
be  assumed  at  five  times  the  crown  thickness.  For  a  pier  between 


DESIGN  OF  VOUSSOIR  ARCHES 


291 


arches  in  a  series  he  suggests  a  thickness  at  top  of  three  and  one-half 
times  the  crown  thickness,  but  places  an  abutment  at  every  third  or 
fifth  span. 

Trautwine  gives  a  method  for  design  of  abutment,  approximately 
as  follows  (see  Fig.  86) : 

Thickness  at  springing  line  in  feet 

,     Radius  .  Rise  .  n  f 
a-b  =  -  —+2feet. 


Layoff  a  —  c  =  rise,  and  c— 


10 

span 


Continue  bd  downward  to  bottom  of  abutment,  and  upward  a 
distance  be  =  rise/2.     From  e 
draw  a  tangent  e—  f  to  the 
extrados. 

It  is  also  required  that 
the  thickness  at  bottom  of 
abutment  gh,  shall  not  be 
less  than  two-thirds  of  the 
height  ag. 

If  the  abutment  is  of 
rough  rubble,  6  inches  is 
added  to  the  thickness  to  in- 
sure full  thickness  in  every 
part.  h 

These  rules  usually  give 
arches  which  are  amply  strong 


FIG.  86. 


for  heavy  railway  service  and  heavier  than  necessary  for  highway 
bridges.  For  structures  of  small  span,  however,  when  voussoir  or 
plain  concrete  arches  are  used,  the  saving  effected  by  paring  them 
down  is  small,  and  rather  heavy  work  is  common  practice. 

162.  Investigation  of  Stability. — After  assuming  dimensions  for 
the  arch  ring  and  abutments,  the  stability  of  the  arch  is  investigated 
by  the  methods  outlined  in  Section  156.  The  stability  of  the  abut- 
ment is  tested  by  continuing  the  line  of  thrust  and  determining 
whether  it  cuts  the  base  of  the  abutment  within  the  middle  third. 
The  sufficiency  of  the  foundation  for  the  abutment  must  also  be 
examined  and  footings  provided  which  will  properly  distribute  the 
pressure  over  the  soil  upon  which  it  is  to  be  placed.  The  following 
example  will  outline  the  method  of  procedare. 

Example. — A  highway  arch  is  to  have  a  span  of  40  feet  and  a  rise 
of  10  feet.  It  is  to  carry  a  moving  load  of  200  pounds  per  square  foot. 


292  MASONRY  ARCHES 

The  depth  of  fill  at  crown  is  2  feet.  The  weight  of  earth  fill  is  100 
and  of  masonry  150  pounds  per  cubic  foot. 

We  will  try  a  segment al  arch.  By  the  Douglas  rule,  the  thickness 
at  crown  would  be  1.4  feet.  By  Trautwine's  formula,  it  would  be 
1.95  feet.  Make  the  crown  thickness  18  inches.  By  the  Douglas 
rule  the  thickness  at  springing  would  be  between  1.5  and  2  times  the 
crown  thickness.  We  will  try  30  inches.  Draw  the  arch  ring  as 
shown  in  Fig.  87,  and  divide  it  into  equal  parts  by  radial  lines.  The 
line  z-t  represents  the  roadway  and  verticals  from  the  points  where 
the  radial  divisions  cut  the  extrados  divide  the  earth  fill  into  parts 
resting  upon  the  sections  of  the  arch  ring.  These  loads,  including  the 
weights  of  the  sections  of  arch  ring,  are  now  computed,  and  their 
vertical  lines  of  action  determined. 

In  finding  the  loads,  it  is  often  convenient  to  draw  the  reduced 
load  contour,  which  is  obtained  by  reducing  the  height  of  the  sections 
go  that  the  volume  contained  by  them  may  be  considered  to  weigh 
the  same  per  unit  as  the  arch  ring.  Thus  if  the  earth  fill  weighs  100 
pounds  and  masonry  150  pounds  per  cubic  foot,  the  height  ax  is 
made  two-thirds  of  az,  and  the  other  verticals  are  reduced  propor- 
tionately, giving  the  volume  a-x-u-g,  which  has  the  same  weight  at 
150  pounds  as  the  earth  fill  at  100  pounds.  In  the  same  way  x-^y^v-u 
represents  the  live  load  which  would  come  upon  half  the  arch  ring 
reduced  to  150  pounds  per  cubic  foot.  In  the  example,  the  loadings 
given  represent  live  load  extending  over  the  left  half  of  the  arch, 
dead  load  only  upon  the  right  half. 

The  horizontal  thrusts  against  the  arch  ring  are  sometimes  com- 
puted by  assuming  that  the  unit  horizontal  thrust  bears  a  definite 
proportion  (usually  about  one-quarter)  to  the  unit  vertical  thrust. 
Thus  in  Fig.  87,  if  the  vertical  load  upon  the  section  a-b  is  5085  pounds 
the  horizontal  component  of  the  load  on  the  section  is 

5085     ap 

— X-r  =  1550  pounds. 
4       pb 

In  the  example,  the  horizontal  components  upon  the  two  lower  divi- 
sions on  each  side  are  used,  those  upon  the  upper  divisions  being  too 
small  to  affect  the  results  appreciably.  The  horizontal  components 
of  the  loads  are  not  usually  considered  in  a  problem  of  this  kind  unless 
the  rise  of  the  arch  is  large  as  compared  with  the  span. 

Having  computed  the  loads,  a  line  of  pressure  may  now  be  drawn 
through  any  three  points  in  the  arch  ring.  Assume  that  it  is  to  pass 
through  the  lower  third  point  of  the  joint  a  on  the  loaded  side,  the 


DESIGN  OF  VOUSSOIR  ARCHES 


293 


294  MASONRY  ARCHES 

middle  point  at  the  crown,  and  the  upper  third  point  at  the  joint  n 
on  the  unloaded  side. 

The  load  line  is  first  plotted  on  a  convenient  scale  by  laying  off  the 
loads  which  come  upon  the  various  sections  in  succession,  n-m,  m-l, 
etc.  ;  n—a  is  now  the  resultant  of  all  the  loads  upon  the  arch  ring.  A 
pole  Of  is  assumed  and  the  strings  O'a,  O'b,  etc.,  drawn. 

The  equilibrium  polygon,  shown  in  broken  lines,  may  now  be 
drawn.  Starting  from  A,  the  lower  third  point  on  joint  a,  with  a  line 
parallel  to  the  string  O'a  to  an  intersection  with  the  line  of  action  of 
the  load  upon  the  section  a-b.  From  this  intersection,  draw  a  line 
parallel  to  O'b  to  intersection  with  the  line  of  action  of  the  load  on 
6-c,  and  continue  it  until  a  parallel  to  O'n  is  intersected  in  N'  upon  a 
line  through  N  parallel  to  the  resultant  n-a. 

Connect  N'  with  A,  and  from  0'  draw  a  line  parallel  to  N'-A 
to  intersection  J  with  the  resultant  n-a  of  the  loads,  thus  dividing 
the  resultant  into  two  reactions,  n-J  and  J-a,  which  would  exist  at 
the  ends  of  the  span  if  the  horizontal  thrust  of  the  arch  be  neglected. 
Join  the  points  A  and  N  and  from  J  draw  a  line  parallel  to  A-N. 
A  pole  lying  upon  this  line  will  give  an  equilibrium  polygon  passing 
through  A  and  N. 

The  distance  of  the  pole  from  J  must  now  be  determined  to  cause 
the  equilibrium  polygon  to  pass  through  the  middle  of  the  crown 
joint.  The  line  g—  a  in  the  force  polygon,  is  the  resultant  of  the  loads 
upon  the  left  half  of  the  arch.  From  the  middle  of  the  crown  section, 
draw  G-G'  ',  parallel  to  g-a,  to  intersection  with  the  trial  equilibrium 
polygon.  Connect  A-G'  and  A-G.  From  0'  draw  O'k  parallel  to 
G'A  to  intersection  with  g-a  in  fc,  and  from  k  draw  k-O  parallel 
to  AG.  The  point  0  where  KO  intersects  JO  is  the  new  pole. 

From  A,  the  new  line  of  thrust  may  now  be  drawn  with  sides  par- 
allel to  the  strings,  Oa,  06,  etc.  This  passes  through  the  points  G 
and  N. 

By  inspection  we  see  that  the  line  of  thrust,  as  thus  drawn,  is 
everywhere  within  the  middle  of  the  arch  ring.  The  thrust  upon 
the  joint  at  a  is  represented  by  the  length  of  the  line  0-a  =  27000 
pounds,  and  the  maximum  unit  compression  is 


The  unit  compression  upon  any  other  joint  may  be  found  in  the  same 
manner. 

The  resultant  pressure  R  upon  the  base  of  the  abutment  is  found 
by  combining  the  weight  W  of  the  abutment  with  the  thrust  0—a  of 


THE  ELASTIC  ARCH 


295 


FIG.  88. 


the  arch  against  the  abutment.  The  footing  under  the  base  of  the 
abutment  should  be  so  designed  as  properly  to  distribute  the  load  over 
the  foundation  soil. 

ART.   46.     THE  ELASTIC  ARCH 

163.  Analysis  of  Fixed  Arch.  —  Reinforced  concrete  arches  are 
commonly  constructed  as  solid  curved  beams  firmly  fixed  to  the 
abutments.   Inan- 
alyzing  them,  it  is 
assumed  that  the 
abutments  are  im- 
movable and  the 
ends  of  the  arch 
firmly  held  in  their 
original  positions. 
Let  Fig.  88  repre- 
sent the  left  half 
of  an  arch,  fixed 
in  position  at  the  end  G-H,  and   carrying  loads  which  produce 
thrusts  and  bending  moments  throughout  the  arch  ring. 

The  arch  may  be  considered  as  made  up  of  a,  number  of  small 
divisions.  Suppose  A  BCD  to  be  one  of  these  divisions,  small 
enough  so  that  its  ends  are  practically  parallel  and  its  section  area 
constant.  The  loads  upon  the  arch  bring  a  bending  moment  upon 
the  division  A  BCD,  which  causes  the  end  CD  to  take  the  posi- 
tion EF. 

Let         M  —  bending  moment  on  the  division; 
s  =  length  of  division,  AD  =  BC; 
e  =  distance  from  center  of  section  to  outside  fiber; 
ds  =  elongation  of  fiber  distant  e  from  neutral  axis; 
/nt  =  Unit  stress  upon  fiber  distant  e  from  neutral  axis; 
k  =  angle  of  distortion,  COE;- 
E  —  modulus  of  elasticity  of  material  ; 
7  =  moment  of  inertia  of  section; 

x  and  y  =  horizontal  and  vertical  coordinates  of  center  of 
section,  0,  with  reference  to  center  of  crown  sec- 
tion, J. 

The  unit  fiber  elongation  in  the  division  A  BCD  is  —  =  —  . 

s      s 


Unit  stress,  fm  = 


also    U--B--E. 

S  S 


296  MASONRY  ARCHES 

Equating  these  and  solving, 


If  the  crown  of  the  arch  be  free  to  move,  the  deflection  of  A  BCD 
into  its  new  form  ABEF  will  bring  the  middle  point  of  the  arch  ring 
J",  to  the  new  position  K.  Let  dx  and  dy  be  the  horizontal  and  ver- 
tical coordinates  of  K  with  respect  to  J.  Then  from  similar  tri- 
angles, JK/OJ  =  dy/x  =  k,  and 

7     Mxs 
dy  =  xk=^j-  ........     (2) 

Similarly, 

Mys 
dx  =  yk=-Jjr.     .....     k.    .     (3) 

As  the  end  section  GH  is  fixed  in  position,  the  summation  of  all 
the  angular  distortions  k,  for  the  left  half  of  the  arch  gives  the  dis- 
tortion at  the  crown  section.  The  summation  similarly  of  those 
for  the  right  half  must  give  the  same  result  with  opposite  sign,  or 
indicating  the  left  and  right  sides  of  the  arch  by  the  subscripts  L 
and  R  respectively,  and  indicating  summation  by  the  sign  2,  we  have 

2kL=  —  Sfc«,  also  2dyL  =  2dyR  and  2dxL  =  -  2dxB. 

Substituting  for  these  distortions,  their  values  as  found  above,  we 
have  for  a  symmetrical  arch  : 

MLs__     MRs 

*~   ~2  '  •  •  •     -*    4 


MLXS_       MRXS 

~:    '~~'  '        *    •       •    • 


and 

MLys  MRys 


If  the  length  of  the  divisions  of  the  arch  ring  be  made  directly 
proportional  to  the  corresponding  values  of  the  moment  of  inertia, 

o  O 

T  =  constant,  the  terms  -^j  in  Equations  (4),  (5),  and  (6)  are  con- 
l  JbL 

stant  and  may  be  eliminated,  and  we  have, 

.......     (7) 

(8) 
.....  (9) 


THE  ELASTIC  ARCH  297 

Fig.  89  represents  a  symmetrical  arch  divided  into  parts  the 
lengths  of  which  are  directly  proportioned  to  the  moments  of  inertia 
of  the  cross-sections  at  their  middle  points.  s/I  =  constant.  Sup- 
pose the  arch  to  be  cut  at  the  crown  and  the  separate  halves  supported 
by  introducing  the  stresses  acting  through  the  crown  section  as 
exterior  forces.  These  may  be  resolved  into  a  horizontal  thrust, 
a  vertical  shear  and  a  bending  moment. 

Hc  =  horizontal  thrust  at  crown; 
Vc  =  vertical  shear  at  crown; 
Mc  =  bending  moment  at  crown. 

Vc  is  considered  to  be  positive  when  acting  in  the  direction 
indicated  by  the  arrows.  Moments  are  taken  as  positive  when  they 


FIG.  89. 


produce  compression  on  the  upper  and  tension  on  the  lower  side  of 
the  section. 

Let       ML  =  bending  moment   on  mid-section   of  any  division 

in  left  half  of  arch; 
M R  =  bending  moment   on  mid-section   of  any  division 

in  right  half  of  arch; 
WIL= moment  at  middle  of  any  division  in  left  half,  caused 

by  external  loads  between  that  division  and  the 

crown  section: 
WR= moment   at  mid-section   of   any  division  in   right 

half,    caused    by    external    loads    between    that 

section  and  the  crown  section; 
X  and  y  =  coordinates  of  middle  point  of  any  division  with 

respect  to  middle  of  crown  section. 

The  bending  moment  at  any  section  of  a  beam  is  equal  to  the 
moment  at  any  other  section  plus  the  moments  of  the  intermediate 
loads  about  the  center  of  the  section.  Therefore, 

ML  =  Mc+Vcx+Hcy-mL, (10) 

MR  =  Mc-Vcx+Hcy-mR (11) 


298  MASONRY  ARCHES 

Substituting  these  values  in  Equations  (7),  (8)  and  (9),  we  have, 

.....  (12) 
(13) 
=  Q.  .  .  .  .(14) 

Solving  for  the  thrusts  and  moments  at  the  crown 


TT  _  ,     . 

2n2y2-2(2y)2 


_ 
c~ 


In  analyzing  an  arch  by  this  method,  the  arch  is  first  divided  into 
a  number  of  parts  in  which  s/I  is  a  constant.  The  loads  upon  the 
divisions  are  then  found  and  mL  and  mR  computed  for  the  several 
centers  of  division.  The  values  of  Hc,  Vc  and  Mc  may  then  be  found 
from  Formulas  (15),  (16)  and  (17),  after  which  the  line  of  thrust 
may  be  drawn  beginning  with  the  known  values  of  H  c  and  Vc  at  the 
crown.  The  moment  Mc  is  due  to  the  eccentricity  of  the  thrust  at 
the  crown,  and  the  point  of  application  for  Hc  may  be  found  by  divid- 
ing Mc  by  Hc.  This  gives  the  vertical  distance  of  Hc  from  the  center 
of  gravity  of  the  crown  section.  For  Mc  positive,  Hc  is  above,  and 
for  Mc  negative,  Hc  is  below  the  center  of  section. 

The  thrust  at  any  section  of  the  arch  may  be  obtained  from  the 
thrust  diagram  as  in  the  voussoir  arch.  The  bending  moment  at 
any  section  is  the  moment  of  the  thrust  upon  the  section  about  the 
center  of  gravity  of  the  section.  The  bending  moment  at  any  section 
may  also  be  obtained  by  the  use  of  Formula  (10)  or  (11). 

In  analyzing  an  arch  bridge  subject  to  moving  loads,  it  is  necessary 
to  assume  different  conditions  of  loading  and  find  the  thrust  and  mo- 
ments resulting  from  each.  For  a  small  arch,  it  is  usually  sufficient 
to  make  the  analysis  for  arch  fully  loaded  and  for  moving  load  over 
one-half  the  arch.  The  maximum  stresses  will  be  more  accurately 
determined  by  dividing  the  moving  load  into  thirds,  and  determining 
the  stresses  with  span  fully  loaded,  one-third  loaded,  two-thirds 
loaded,  center  third  loaded,  and  with  two  end  thirds  loaded.  If 
complete  analysis  be  made  for  the  arch  under  dead  load  alone,  for 
live  load  over  one  end  third,  and  live  load  over  the  middle  third,  the 
results  of  these  three  analyses  may  be  combined  to  give  the  five 
conditions  of  loading  above  mentioned. 


THE  ELASTIC  ARCH  299 

164.  Effect  of  Changes  of  Temperature. — A  rise  in  temperature 
tends  to  lengthen  and  a  fall  in  temperature  to  shorten  the  span. 
If  the  ends  of  the  arch  ring  are  rigidly  held  in  position,  the  tendency 
to  change  in  length  is  resisted  by  moments  and  horizontal  thrusts 
at  the  supports,  which  produce  moments  and  thrusts  throughout  the 
arch  ring. 

If  the  arch  ring  were  not  restrained,  a  rise  in  temperature  of 
t  degrees  would  cause  an  increase  in  length  =  CtL ;  L  being  the  length 
of  span  and  C  the  coefficient  of  expansion  of  the  material.  The 
moments  throughout  the  arch  ring  are  therefore  those  which  cor- 
respond to  an  actual  change  in  length  of  span  =  C£L,  or  from  For- 
mula (3) 


From  this,  for  a  symmetrical  arch  ring 

MLys  _     MRys  _  ClL 

and 

As  there  are  no  exterior  loads,  mLj  and  Vc  are  each  equal  to  zero, 
and  Formula  (10)  becomes  ML  =  Mc-\-Hcy.  Substituting  this  in 
(18)  and  (19)  and  solving,  we  have 

=  EI          CtLn 

nc          s    *0^-v..2       0/V.A2 \"W 


The  line  of  thrust  consists  of  a  single  force  Hc,  and  is  applied 
on  a  horizontal  line  at  a  distance,  e  =  2y/n,  below  the  middle  of  the 
crown  section.  The  bending  moment  at  any  section  due  to  Hc  is 

The  direct  thrust  upon  any  section  of  the  arch  ring  is  the  com- 
ponent of  Hc  normal  to  the  section. 

For  temperatures  below  the  normal,  Hc  will  be  negative  and  may 
be  found  from  Formula  (20)  by  giving  t  the  negative  sign. 

165.  Effect  of  Direct  Thrust. — Axial  thrusts  on  the  arch  ring 
produce  compressive  stresses  on  the  various  sections  and  also  tend 
to  shorten  the  arch  ring.  As  the  span  length  does  not  change,  this 


300  MASONRY  ARCHES 

tendency  to  become  shorter  causes  stresses  in  the  arch  ring  in  the 
same  manner  as  does  lowering  temperature.  If  fe  lb./in.2  be  the 
average  unit  compression  due  to  axial  thrust,  the  arch  ring  if  unre- 
strained would  be  shortened  an  amount  dx=fcI/E,  from  which, 

rr          I    fcLn 

iic  =--0    ^  o 

s  2n2y2 


and 

M'=n?"     I    •"•/•'••.    •    •     (23) 

As  the  unit  stress  fc  is  not  uniform  through  the  arch  ring,  a  value 
obtained  by  finding  the  stresses  at  several  points  and  averaging 
them  may  be  used. 

The  stresses  due  to  shortening  of  the  arch  ring  are  comparatively 
small  and  are  often  neglected  in  the  analysis  of  ordinary  arches; 
in  some  instances,  however,  they  may  be  considerable. 

ART.   47.     DESIGN   OF  REINFORCED    CONCRETE  ARCH 

166.  Selection  of  Dimensions. — In  designing  an  arch,  it  is  neces- 
sary to  first  assume  dimensions  for  the  arch  ring,  and  then  investigate 
for  the  strength  of  the  arch  and  the  suitability  of  the  assumed  dimen- 
sions to  the  conditions  of  service.  The  methods  of  investigation 
usually  employed  are  indicated  in  Art.  46.  The  investigation  will 
show  whether  changes  in  form  or  thickness  should  be  made  in  the 
arch  ring.  The  shape  of  the  arch  should  be  such  as  to  fit  as  closely 
as  possible  the  lines  of  pressure,  and  the  thickness  should  be  such  as 
to  give  allowable  stresses  under  all  conditions  of  loading. 

Example. — As  an  illustration  of  the  method  of  investigation,  we 
will  assume  an  arch  of  60  feet  clear  span  and  12  feet  rise,  to  carry 
a  live  load  of  100  pounds  per  square  foot  of  road  and  a  solid  spandrel 
filling,  2  feet  deep  over  the  crown,  weighing  100  pounds  per  cubic  foot. 
For  ordinary  arches  with  solid  spandrel  filling,  a  three-centered 
intrados,  with  radii  at  the  sides  from  three-fifths  to  three-fourths  that 
at  the  crown,  is  apt  to  give  better  results  than  a  segmental  intrados. 
We  will  use  an  intrados  composed  of  three  arcs  tangent  to  each  other 
at  the  quarter  points  with  radii  of  52.5  feet  and  31.25  feet  respect- 
ively (see  Fig.  91). 

/—     L      W      W 

Weld's  formula l  for  the  crown  thickness  is  t  =  V ^+TTJ + ^T^+TT^ 

in  which 

?  l  Engineering  Record,  Nov.  4,  1905. 


DESIGN  OF  REINFORCED  CONCRETE  ARCH  301 

t  =  the  crown  thickness  in  inches; 
L  =  clear  span  in  feet; 
TF  =  live  load  in  pounds  per  square  foot; 
W  =  weight  of  fill  at  crown  per  square  foot. 

Applying  this  formula,  we  find  a  crown  thickness  of  16  inches.  The 
thickness  of  the  arch  ring  should  increase  from  the  crown  to  the  spring- 
ing line;  the  thickness  at  the  quarter  point  may  be  made  a  little 
greater  than  that  at  the  crown  (about  1J  to  1J  times).  We  will 
assume  a  thickness  at  the  quarter  point  of  21  inches,  and  at  the  spring- 
ing line  of  45  inches.  The  extrados  will  now  consist  of  three  arcs 
tangent  to  each  other  at  the  quarter  points  and  giving  the  desired 
thicknesses.  Fig.  117  shows  the  arch  ring  as  assumed. 


FIG.  90. 


The  reinforcement  may  be  assumed  at  from  .4  to  .7  per  cent  of  the 
area  of  the  section  at  the  crown,  to  be  placed  at  both  extrados  and 
intrados.  We  will  use  f-inch  round  bars  spaced  7  inches  apart. 

167.  Division  of  Arch  Ring. — Having  chosen  the  form  and  dimen- 
sions of  the  arch  ring,  it  is  necessary  to  divide  the  ring  so  that  the 
lengths  of  the  divisions  shall  be  directly  proportional  to  the  moments 
of  inertia  of  their  mid-sections,  s/I  =  constant.  This  may  be  done 
by  trial,  assuming  a  division  next  the  crown,  determining  the  value 
of  s/7  for  the  assumed  division,  and  finding  the  corresponding  lengths 
of  other  sections  toward  the  abutment.  Then  changing  the  first 
assumption  as  may  seem  necessary  to  make  the  division  come  out 
properly  at  the  abutment. 

More  easily,  the  division  may  be  made  graphically  as  shown  in  Fig. 
90.  The  line  a-k  is  laid  off  equal  in  length  to  half  the  arch  axis  (34.52 
feet).  The  moments  of  inertia  are  then  computed  at  several  points 


302  MASONRY  ARCHES 

along  the  arch  axis,  and  their  amounts  laid  off  normally  to  the  line 
a-k,  and  the  curves  of  moment  of  inertia  drawn  through  the  points 
so  located. 

A  trial  diagonal  is  then  drawn  from  A  to  intersection  with  the 
curve  in  the  point  B.  A  vertical  from  B  is  drawn  to  intersection 
with  the  upper  curve,  and  a  second  diagonal  parallel  to  A-B,  cutting 
the  lower  curve  in  C.  Continue  successive  diagonals  and  verticals 
until  the  end  k  is  reached.  If  these  do  not  come  out  accurately  at  the 
end  k  the  inclination  of  the  diagonals  may  be  varied  until  the  division 
of  a-k  is  made  into  the  correct  number  of  parts.  This  divides  a-k 
into  lengths  which  are  proportional  to  the  average  of  the  moments  of 
inertia  at  the  ends  of  the  divisions. 

The  lengths  of  the  divisions,  a— 6,  b— c,  etc.,  are  now  transferred 
to  the  arch  axis.  The  axis  of  the  arch  in  Fig.  91  is  thus  laid  off 
into  ten  divisions  on  each  side  of  the  crown  section.  The  con- 
stant ratio  s/I  is  found  to  be  5.1,  all  measurements  being  taken  in 
feet. 

The  middle  point  of  the  arch  axis  in  each  division  is  now  located, 
and  the  values  of  x  and  y  are  determined  with  reference  to  the  middle 
of  the  crown  section.  These  values  and  their  squares  are  tabulated 
in  Table  XXI  for  use  in  the  computations. 

168.  Analysis. — If  vertical  lines  be  drawn  through  the  points  of 
division  of  the  arch  axis,  the  weight  of  the  portion  of  masonry  and 
spandrel  filling  included  between  each  pair  of  lines  may  be  considered 
as  the  dead  load  resting  upon  the  included  division.  The  live  load  is 
similarly  divided  for  the  portion  of  the  arch  over  which  it  is  considered 
as  acting.  In  Fig.  91  the  live  load  is  taken  as  extending  over  the  left 
half  of  the  arch,  and  the  loads  are  as  indicated.  The  values  of  m^ 
and  mR  are  now  computed  and  placed  in  Table  XXI,  and  include  in 
each  instance  the  moments  of  all  loads  between  the  division  con- 
sidered and  the  crown  section  about  the  center  of  division.  The 
quantities  mLx,  mRx,  mLy,  and  mRy  may  now  be  computed  and  placed 
in  the  table,  and  the  summations  of  the  various  columns  obtained. 
These  substituted  in  Formulas  (15),  (16)  and  (17)  give, 

_  10(2375207+ 1989744)  -(512291  +425771)  17.09 
Hc~  2X10X80.85-2X17.09X17.09 

T/      10408051-8686133 

Fc=         2X1769.5          =+487  pounds, 


DESIGN  OF  REINFORCED  CONCRETE  ARCH 


303 


304 


MASONRY  ARCHES 


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DESIGN  OF  REINFORCED  CONCRETE  ARCH  305 

Having  obtained  the  thrusts  and  moment  at  the  crown,  we  may 
now  proceed  to  find  the  thrusts  and  moments  at  any  other  section 
desired.  The  thrusts  are  obtained  graphically  by  drawing  the  line 
of  pressure.  The  load  line  is  first  constructed,  as  shown  by  the  ver- 
tical line  a-u.  Vc  and  Hc  are  laid  off  from  the  mid-point  k  of  this 
line,  thus  locating  the  pole  0.  The  force  diagram  is  then  completed 
by  drawing  connections  from  0  to  the  extremities  of  the  various  loads. 

The  equilibrium  polygon  is  now  drawn,  beginning  with  the  crown 
thrust  (0-K),  the  point  of  application  of  which  is  at  a  point  e  = 

7     =+0.05  foot  above  the  center  of  the  crown  section.     The 

thrust  upon  each  section  is  now  shown  in  amount  by  the  length  of  the 
line  from  0  to  the  division  in  the  load  line,  and  its  line  of  action  by  the 
corresponding  line  in  the  equilibrium  polygon  (or  line  of  pressure). 

The  bending  moment  at  any  section  may  be  found  by  multiplying 
the  thrust  upon  the  section  by  its  perpendicular  distance  from  the 
center  of  section,  or  it  may  be  computed  by  the  use  of  Formula  (10) 
or  (11).  Usually  the  formula  is  employed  and  the  measurement  of 
the  eccentricity  used  as  a  check. 

169.  Computation  of  Stresses.  —  At  the  crown,  the  stress  due  to 
direct  thrust  is 

,     thrust      26715 
^ 
for  the  moment, 

/c= 

This  gives 

124+21  =  +145  lb./in.2  at  the  extrados 
and 

124-21  =  +103  lb./in.2  at  the  intrados. 

At  the  left  support,  by  Formula  (10), 

Mz,=  1247+26715X11.7+487X31.25-349930  =  -20899  ft.-lb. 

and  the  measured  thrust  =  40300  pounds,  giving  an  eccentricity 
of  -20899/40300  =-.5  foot.  This  may  be  checked  by  measure- 
ment. Then  for  thrust, 


and  for  moment, 

r     20899X12X21  2 

/c=         79098  -671b/m.2, 

giving  at  the  extrados 

fe  =  80-  67  =  +  13  lb./in.2 


306  MASONRY  ARCHES 

and  at  the  intrados 

fc  =  80+67=  +147  lb./in.2 
At  the  right  support,  by  Formula  (11), 

MR=  1247+26715X11.7-487X3125-303226=  -4632  ft.-lb. 
The  measured  thrust  is  39,200,  and  the  eccentricity 

4632 


39200 


-.12  foot. 


39200 
For  thrust,  fc  =  .  =  78  lb./in.2,  and  for  moment,  fc  —  —  15  lb./in.2 


This  gives  at  extrados  fc  =  63  lb./in.2,  and  at  intrados  fc=  +93  lb./in.2 
At  point  SL, 

ML=  1247+26715X2.25-487X15.88-70608=-  1520  ft./lb. 
Thrust  =  27600  pounds 
,      27600 


„  .      -1520X12X10.5 

For  moment,  /c=  10964  =      ^/m.  2; 

this  gives  at  extrados  fc  =  93  lb./in.2,  and  at  intrados  fc  =  127  lb./in.2 
At  point  SR,  in  the  same  manner,  we  have  at  extrados,  /c  =  58 

lb./in.2  and  at  intrados  fc  =  150  lb./in.2 

Full  Load.  —  When  the  live  load  extends  across  the  whole  span 

of  the  arch,  the  loading  is  symmetrical  and  the  values  given  in 

Table  C  for  mR  become  equal  to  those  for  mL.     We  then  have 


2X10X2375207-2X512291X17.09 
-.  85-2X17.  09X17.  09 


The  force  diagram  is  now  drawn  for  one-half  of  the  arch,  and  the 
equilibrium  polygon  may  be  drawn  as  in  the  case  of  partial  load- 
ing. To  avoid  confusion  it  is  not  drawn  in  Fig.  91.  The  stresses 
in  the  crown  section  due  to  this  loading  are 

,      29030  2  1662X12X9  .     ,-.    2 

/         and  /c=     ~         --  =  +281b./m.2 


DESIGN  OF  REINFORCED  CONCRETE  ARCH  307 

This  gives  at  extrados,  total  fe=  131+28=  +159  lb./in.2,  and  at 
intrados,  total  fe  =  131  -  28  =  103  lb./in.2 

At  section  8,  M=  1662+29030X2.25-70608=  -3629  ft.-lb. 
The  thrust  is  30,350  pounds,  and  the  resulting  unit  stresses  at  extra- 
dos fc=  120  -36  =  84  lb./in.2  and  at  intrados  fe  =  156  lb./in.2 

At  the  support  in  the  same  manner,  the  thrust  is  42,600  pounds, 
and  the  moment,  M=  1662+29030X11.7-349930=  -8617  ft./lb. 
from  which  at  extrados,  fc  =  84  —  27  =  57  lb./in.2,  and  at  intrados 
fc=  111  lb./in.2 

Temperature  Stresses.  —  If  we  assume  that  a  rise  in  temperature 
of  20°  above  the  normal  may  take  place,  Formula  (20)  gives 

„      288000000  .0000055X20X62.5X10 

Hc=  "    X 


2X10X8Q.  85-2X17.  09X17.  09 
and  (21), 

,        -3770X17.09  6448  , 

Mc  =  -   —    -  =-6448  ft.-lb.      e=~=  -1.71  feet. 


The  equilibrium  polygon  is  a  horizontal  line  1.71  feet  below  the 
center  of  the  crown  section,  and  the  bending  moment  at  any  section 
of  the  arch  ring  is  equal  to  3770  tunes  the  vertical  distance  from 
the  center  of  section  to  the  line  of  thrust.  At  point  8  the  moment 
due  to  change  of  temperature  is 

3770  X  (2.25-  1.71)  =  +2037  ft.-lb. 
and  at  point  a, 

M  =  3770X  (11.7-  1.71)  =37,696  ft.-lb. 

The  stresses  at  the  crown  section  are,  at  extrados 

fc  =  17  -112  =-95  lb./in2, 
and  at  intrados 

fe  =  17+  112  =+129  lb./in.2 

The  normal  thrust  on  section  at  point  8  is  the  component  of 
Hc  normal  to  the  section,  given  in  diagram  in  Fig.  118,  =3345 
pounds.  At  section  a,  thrust  =  2510.  These  thrusts  and  moments 
give  at  8,  for  extrados  fe  =  14  +24  =  38  lb./in.2;  for  intrados, 
/«  =  14  -24  =-10  lb./in.2  at  support;  extrados  fc  =+  127  lb./in.2; 
intrados,  /«=  -  113  lb./in.2 

For  a  fall  in  temperature  the  stresses  are  equal  and  opposite 
to  those  for  rising  temperature. 

Arch  Shortening.  —  The  effect  of  direct  thrust  in  shortening  the 
span  of  the  arch,  taking  average  unit  compression  as  100  lb./in.2 


308 


MASONRY  ARCHES 


average  of  stresses  at  crown,  point  8  and  support  under  one-half 
live  load  by  Formula  (23), 


J_  100X144X62.5X10 
>.l'  1033 


=  —17 10  pounds. 


This  is  applied  on  the  same  line  as  the  temperature  thrust  and  the 
stresses  are  therefore  equal  to  1710/3770  =  .45  of  those  for  falling 
temperature. 

Table  XXII  shows  the  computed  stresses  upon  the  sections  at 
crown,  at  point  8  and  at  supports.  Examination  of  this  table  shows 
that  the  unit  compression  is  nowhere  excessive.  Tension  of  34  lb./in.2 
occurs  at  the  intrados  in  the  crown  section  at  low  temperature.  This 
is  too  small  to  cause  cracking  in  the  reinforced  section.  The  tension 
of  150  lb./in.2  at  the  extrados  of  the  support  section  would  possibly 
crack  the  concrete.  The  compression  at  the  intrados  under  the  same 
conditions  would  be  331  lb./in.2,  and  the  reinforced  section  would  be 
capable  of  bearing  the  load  if  the  steel  be  assumed  to  carry  all  the 
tension.  It  might  be  desirable,  however,  to  introduce  additional 
reinforcement  at  this  point  to  lessen  the  unit  tension  in  the  steel  and 
prevent  cracking,  and  these  negative  stresses  might  also  be  eliminated 
by  slightly  modifying  the  form  of  the  arch,  increasing  the  radius  at 
the  crown  and  decreasing  those  at  the  ends,  although  the  form  as 
shown  agrees  fairly  well  with  the  lines  of  thrust. 

TABLE  XXII.— STRESSES   IN   ARCH  SECTIONS,   LB/IN.2 


CROWN. 

POINT  8ft. 

POINT  SL. 

SUPPORT  R. 

SUPPORT  L. 

Character  of  Load. 

Extr. 

Intr. 

Extr. 

Intr. 

Extr.- 

Intr. 

Extr. 

Intr. 

Extr. 

Intr. 

Dead  and  one-half 

live  load  

+145 

+  103 

+58 

+150 

+93 

+  127 

+  63 

+   93 

+13 

+  147 

Dead  and  full  live 

load 

+159 

+103 

+84 

+156 

+84 

+156 

+  57 

+  111 

+57 

+  111 

High  temperature 

-  95 

+129 

+38 

-  10 

+38 

-  10 

+127 

-113 

+127 

-113 

Low  temperature  . 

+129 

-  95 

-10 

+  38 

-10 

+  38 

-113 

+127 

-113 

+  127 

Arch  shortening  .  . 

+  58 

-  42 

-  5 

+  17 

-  5 

+  17 

-  50 

+  57 

-  50 

+  57 

Maximum  stresses 

+346 

+180 

+117 

+211 

+126 

+211 

+140 

+295 

+184 

+337 

Minimum  stresses 

+108 

-  34 

+  43 

+157 

+  69 

+134 

-106 

+  37 

-150 

+  55 

TYPES  OF  CONCRETE  ARCHES  309 


ART.  48.    TYPES   OF   CONCRETE  ARCHES 

170.  Arrangement  of  Spandrels. — In  ordinary  bridges  of  short 
span,  solid  arches  with  filled  spandrels  are  commonly  employed,  as 
shown  in  the  example  of  the  last  article.     In  such  arches,  spandrel 
walls  are  used  to  retain  the  filling  above  the  arch  ring.     These  are 
usually  light  reinforced  walls  and  must  be  designed  to  resist  the 
side  pressure  of  the  filling  with  its  live  load.      When   the  depth 
of  filling  is  considerable,   a  thin  wall  with   counterforts  is  often 
employed. 

For  larger  bridges,  and  where  heavy  filling  would  be  required,  open 
spandrels  are  often  used.  In  these,  the  floor  is  usually  carried  by 
slabs  and  the  loads  are  brought  vertically  upon  the  arch  ring  by  cross 
walls.  In  such  arches,  the  dead  loads  with  their  lines  of  action  are 
definitely  known,  and  the  use  of  influence  lines  gives  an  accurate 
method  of  determining  the  effect  of  moving  loads  at  any  point  of  the 
road  surface. 

In  a  large  open  spandrel  arch,  the  arch  ring,  instead  of  being  solid, 
is  frequently  composed  of  two  or  more  longitudinal  ribs.  The  bridge 
floor  is  supported  by  beams  and  slabs,  and  the  load  transferred  to  the 
ribs  by  a  series  of  columns.  The  determination  of  stresses  is  made 
in  the  same  manner  as  for  the  solid  arch,  the  whole  section  of  the  arch 
rib  being  used  to  carry  loads  brought  by  the  columns,  instead  of 
determining  loads  and  sections  for  a  1-foot  slice  of  the  arch  ring.  The 
loads  must  be  brought  upon  the  ribs  axially,  so  as  to  produce  no 
horizontal  bending  moment,  and  the  width  of  the  rib  must  be  suffi- 
cient to  enable  it  to  act  as  a  column  between  points  of  support.  The 
width  may  increase  from  the  crown  to  the  support  so  as  to  maintain 
a  proper  relation  between  width  and  depth. 

171.  Methods  of  Reinforcement. — There  are  several  methods  of 
arranging  the  reinforcement  in  concrete  arches.     Numerous  patented 
systems  are  more  or  less  in  use,  while  many  designers  place  reinforcing 
bars  in  any  way  that  seem  to  best  meet  their  needs  without  following 
any  particular  system. 

The  Monier  system  was  the  earliest  type  invented,  and  consists 
in  placing  wire  netting  near  the  surfaces  of  the  arch  at  both 
intrados  and  extrados.  This  system  has  been  quite  largely  used  in 
Europe. 

The  Melan  arch  has  steel  ribs,  consisting  of  bent  I-beams,  or  of 
built-up  lattice  girders,  spaced  2  or  3  feet  apart,  extending  from  abut- 
ment to  abutment,  they  are  self-supporting,  and  may  sometimes  be 
used  to  carry  the  forms  in  placing  the  concrete  for  the  arch  ring. 


310  MASONRY  ARCHES 

Many  Melan  arches  have  been  constructed  in  the  United  States, 
most  of  those  built  previous  to  1900  being  of  this  type. 

In  the  Thacher  system,  steel  bars  are  used  in  pairs,  one  immediately 
above  the  other,  near  the  extrados  and  intrados,  the  bars  being  inde- 
pendent of  each  other.  Several  modifications  of  the  Thacher  system 
have  been  patented,  in  which  the  rods  alternate  in  position  or  are 
connected  in  some  way. 

In  other  systems,  attempts  are  made  to  use  single  tension  bars, 
bent  to  pass  from  the  extrados  at  certain  points  to  the  intrados 
at  others  as  the  occurrence  of  tensions  may  require. 

When  the  stresses  upon  the  concrete  in  an  arch  are  kept  within 
proper  limits,  the  unit  stresses  upon  the  steel  are  very  small,  and 
more  steel  must  be  used  than  would  be  necessary  to  carry  the  tensions 
if  reasonable  unit  stresses  for  the  steel  could  be  allowed.  The  steel 
is  not  therefore  economically  used  in  carrying  stresses.  It  is  rather 
intended  to  give  added  security  against  unforeseen  contingencies, 
preventing  cracks  in  the  concrete,  and  guarding  against  distortions 
due  to  slight  settlement  of  foundations  or  structural  defects. 

172.  Hinged  Arches. — Hinges  are  frequently  used  in  arches  for  the 
purpose  of  making  the  stresses  more  nearly  determinate,  they  give 
definite  points  through  which  the  line  of  pressure  must  pass. 

Three-hinged  Arches. — Three  hinges  are  usually  employed  and 
have  the  advantage  of  fixing  the  line  of  pressure  so  as  to  make  it 
statically  determinate.  It  is  assumed  that  the  hinge  acts  without 
friction  and  the  line  of  pressure  passes  through  the  center  of  the 
hinges.  Making  this  assumption,  the  horizontal  and  vertical  com- 
ponents of  the  thrusts  at  the  supports  may  be  determined  by  means 
of  moments  about  the  hinge  centers.  In  large  arches  the  hinges  have 
the  advantage  of  eliminating  the  temperature  stresses.  Slight  settle- 
ment of  the  foundations  may  occur  in  hinged  arches  without  sensibly 
changing  the  stresses,  while  the  accuracy  of  the  computed  stresses 
in  a  solid  arch  is  dependent  upon  the  rigidity  of  the  supports.  Hinges 
are  usually  expensive  to  construct,  and  the  form  of  the  arch,  if  eco- 
nomically designed,  is  not  so  graceful  as  that  of  a  solid  arch. 

Two-hinged  Arches. — Two  hinges  are  sometimes  used  at  the 
supports  without  the  crown  hinge.  Two  points  upon  the  line  of 
pressure  are  thus  fixed  and  the  vertical  components  of  the  end 
thrusts  may  be  found  by  moments  about  the  hinges.  As  the  span 
of  the  arch  remains  unchanged  upon  the  application  of  the  loads, 
Formula  (14)  of  Section  163  applies  to  this  case,  or 

=  0 (14) 


TYPES  OF  CONCRETE  ARCHES  311 

Let    RL  =  vertical  component  of  the  thrust  at  left  support; 

Mw= moment  at  crown  of  all  loads  between  crown  and  left 

support; 

L/2  =  half  span  of  the  arch  axis; 
h  =  rise  of  the  arch  axis. 

Then  using  the  same  notation  as  for  the  solid  arch, 

Mc  =  RLL/2-Hch-mw (23) 

Substituting  this  in  (14),  we  have  for  arch  with  vertical  loading, 

rr  _  2mLy + 2mRy +2mw 
22y2-2h 

The  thrusts  and  moments  may  now  be  determined  in  the  same 
manner  as  for  the  solid  arch. 

173.  Unsymmetrical  Arches. — The  formulas  of  Art.  46  apply  only 


FIG.  92. — Unsymmetrical  Arch. 

to  arch  rings  which  are  symmetrical  with  respect  to  the  crown  sec- 
tion. It  is  frequently  necessary  or  desirable  to  construct  arches 
which  for  topographical  reasons  are  not  alike  upon  the  two  sides  of  the 
crown.  In  these  arches  if  s/I  is  made  constant  for  the  whole  arch 
a  division  may  not  come  at  the  crown  section,  the  values  of  x  and  y 
will  not  be  the  same  upon  the  two  sides  of  the  section  nearest  the 
crown,  and  the  formulas  produced  as  in  Section  164  become  quite 
complicated. 

For  this  case,  the  origin  of  coordinates  may  be  taken  at  the  middle 
of  the  lower  support,  as  in  Fig.  92. 

Let         M  =  bending  moment  at  mid-point  of  any  division ; 
ML  =  bending  moment  at  left  support ; 
VL= vertical  component  of  thrust  at  left  support; 
HL  =  horizontal  component  of  thrust  at  left  support; 


312  MASONRY  ARCHES 

x  and  y  =  coordinates  of  mid-points  of  divisions  from  center 

of  left  support; 
m  —  moment  at  any  mid-point  of  division  of  all  exterior 

loads  between  the  division  and  the  left  support. 
Then,  using  the  method  of  Section  167,  we  have  2M  =  0,  2Mx  =  0, 
2My  =  Q,  and 

M=ML+Vtx-HLy-m  ......     (25) 

From  this  by  substitution  we  obtain 

nML+VL2x-HL2y-2m        =  0; 


-  2mx  =  0. 
Combining  these  and  solving,  we  find 

Jn^x2-(^x)2][^m^y-n^my]-[n^xy-Zx^y][^m^y-n^mx]   , 


=  - 

(2g) 

Having  found  the  values  of  HL,VL  and  MLj  the  moment  at  any 
section  may  be  calculated  by  Formula  25,  and  the  line  of  pressure 
may  be  drawn,  beginning  at  the  left  support. 

The  line  of  thrust  due  to  change  of  temperature  will  be  parallel 
to  a  line  joining  the  ends  of  the  arch  axis. 

If  L  =  the  horizontal  span  of  the  arch  axis,  and  J  =  the  height 
of  its  right  end  above  its  left  end,  using  the  notation  of  Section  168, 
we  have 


71 

and 

e  rtJ.vt 

(30) 


174.  Arches  with  Elastic  Piers. — In  the  ordinary  theory  of  the 
elastic  arch,  the  supports  are  supposed  to  be  rigid  and  unyielding. 
This  can  never  be  strictly  true,  but  it  is  practically  correct  where 
good  foundations  are  obtained  and  a  sufficient  weight  of  abutment 
is  used. 


TYPES  OF  CONCRETE  ARCHES 


313 


In  the  construction  of  a  series  of  arches,  light  piers  are  sometimes 
employed  to  carry  the  vertical  loads,  the  arches  being  depended 
upon  to  carry  the  horizontal  reactions.  In  such  systems,  the  tops 
of  the  piers  are  subject  to  lateral  motion  which  may  materially  affect 
the  stresses  in  the  arch  rings. 

The  bases  of  the  piers  must  always  be  designed  so  that  the  result- 
ant of  the  loads  fall  within  their  middle  thirds,  so  that  the  bases  will 
remain  in  contact  with  the  foundations  throughout.  When  this  is 
the  case,  the  piers  become  cantilevers  held  firmly  at  their  bases  and 
fixed  between  the  arches  at  their  upper  ends. 

When  the  structure  is  composed  of  nearly  equal  spans,  and  the 
thrust  against  the  pier  does  not  differ  greatly  on  the  two  sides  under 
dead  load,  the  effect  of  the  flexibility  of  the  pier  may  be  investigated 
for  moving  loads  by  a  method 
of  approximation.  In  Fig.  93, 
TL  and  TR  are  the  thrusts  of 
the  spans  upon  the  left  and 
right  respectively  and  R  is  their 
resultant  acting  upon  the  pier. 
The  maximum  load  is  supposed 
upon  the  left  span  and  dead 
load  only  upon  the  right.  The 
difference  of  the  horizontal 
components  of  TL  and  TR, 
HL-HR,  is  the  horizontal  com- 
ponent of  R. 

This  is  applied  at  the  top  of 
the  pier,  causing  the  pier  to  act 
as  a  cantilever  fixed  at  the  bot- 
tom. If  we  assume  that  the  top  of  the  pier  is  firmly  held  by  the 
ends  of  the  arch,  so  that  no  rotation  takes  place,  the  top  of  the  pier 
will  have  only  a  horizontal  motion.  The  effect  of  this  motion  is  to 
lengthen  the  span  of  the  arch  upon  the  left  of  the  pier  and  decrease 
that  of  the  arch  upon  the  right,  which  will  decrease  the  value  of  HL 
and  increase  that  of  HR. 

Let  Q  =  the  horizontal  motion  at  top  of  pier; 

/i  =  the  height  of  pier; 

Iv  =  average  moment  of  inertia  of  horizontal  sections  of  pier. 
The  crown  thrust  for  the  span  on  the  left  then  becomes, 


FIG. 


Hc  = 


nQEI/s 


(31) 


314  MASONRY  ARCHES 

and  for  the  span  upon  the  right, 


nQEI/s 


c~  2n2y2-2(2y)2 

^_(HL-HRW 
12EIP 

The  formulas  for  Vc  and  M  c  are  unchanged  by  the  motion  of  the  top 
of  the  pier,  and  are  the  same  as  for  the  arch  with  fixed  ends. 

If  values  of  HL  and  HR  be  found  by  the  formula  for  fixed  supports, 
and  the  value  of  Q  corresponding  to  their  difference  computed,  the 
actual  value  of  Q  will  be  less  than  the  computed  value,  and  a  trial 
value  may  be  used  in  obtaining  new  values  of  HL  and  HR,  until  the 
values  of  the  three  quantities  are  in  fair  agreement. 

The  above  is  inaccurate  in  neglecting  possible  bending  at  the 
top  of  the  pier.  If  the  top  of  the  pier  in  Fig.  93,  be  held  against 
rotation,  a  bending  moment  will  be  produced  in  section  A-B  equal 
to  MJ>=(HL-HR)h/2.  The  actual  bending  moment  in  the  section 
A-B  is  that  produced  by  the  eccentricity  of  the  resultant  of  the 
thrusts  of  the  arches  against  the  pier,  or  Mp  =  Re.  In  order  that 
no  tendency  to  rotate  exist,  Re  should  not  be  less  than  (HL-HR)h/2. 
The  error  due  to  this  cause  may  usually  be  made  insignificant  by 
careful  design. 

Methods  of  analyzing  arches  with  elastic  piers  may  be  found 
in  the  works  of  Melan1  and  Hool.2  In  a  paper  by  A.  C.  Janni 
in  the  Journal  of  the  Western  Society  of  Engineers,  May,  1913,  a 
graphical  method  of  analysis  is  outlined,  by  the  use  of  the  ellipse 
of  elasticity,  which  may  be  applied  to  a  system  of  arches  with  elastic 
piers.  These  methods  are  complicated  and  cannot  be  discussed 
here  ;  they  all  involve  assumptions  which  make  it  necessary  to  exercise 
care  in  their  application. 

ART.   49.     OTHER   METHODS   OF  ANALYSIS 

175.  Analysis  by  Influence  Lines.  —  In  important  structures,  other 
conditions  of  loading  than  those  mentioned  in  the  preceding  para- 
graphs may  be  desirable,  and  a  more  complete  analysis  may  be  ob- 
tained by  determining  the  effect  of  individual  loads  at  the  various 
points  of  loading,  which  is  accomplished  by  using  influence  lines  to 
determine  the  effect  of  a  unit  load  at  each  load  point.  In  open  span- 
drel arches,  when  the  loads  are  brought  upon  the  arch  ring  at  defi- 

1  Plain  and  Reinforced  Concrete  Arches,  by  J.  Melan,    translated  by  D.  B 
Steinman,  New  York,  1915. 

2  Reinforced  Concrete  Construction,  Vol.  Ill,  by  George  A.  Hool,  New  York, 
1915. 


OTHER  METHODS  OF  ANALYSIS 


315 


nite  points,  by  vertical  walls  or  columns,  this  method  may  be  easily 
applied. 

Fig.  94  represents  an  arch  80  feet  long,  16  feet  rise;  depth  at 
crown,  2  feet;  at  springing  line,  2.8  feet.  It  is  reinforced  with  1.6 
in.2  of  steel  per  foot  of  arch,  placed  2.5  inches  from  both  extrados 
and  intrados.  The  loads  are  assumed  to  be  applied  through  cross 
walls  at  points  10  feet  apart. 


FIG.  94. 

The  arch  ring  is  divided  into  ten  parts  on  each  side  of  the  crown, 
so  that  the  ratio  s/I  is  constant;  s  being  the  length  of  division  and  / 
the  moment  of  inertia  at  the  middle  of  the  division.  Using  the 
notation  of  Section  167,  the  values  of  x  and  y  for  centers  of  the 
various  divisions  are  as  given  in  Table  XXIII. 

TABLE  XXIII 


Points. 

X 

y 

z2 

y* 

1 

1.42 

0.02 

2.0 

0.0 

2 

4.39 

0.23 

19.3 

0.1 

3 

7.58 

0.50 

57.5 

0.2 

2nS?/2-2(S?/)2=3928 

4 

11.01 

1.06 

115.8 

1.1 

5 

14.70 

1.89 

216.1 

3.6 

6 

18.67 

3.09 

348.6 

12.1 

2Sz2  =  8935.8 

7 

22.94 

4.73 

502.5 

22.4 

8 

27.50 

6.94 

756.3 

48.2 

2n  =  20. 

9 

32.35 

9.86 

1046.5 

97.2 

10 

37.46 

13.72 

1403.3 

188.2 

S 

178.02 

42.04 

4467.9 

373.1 

316 


MASONRY  ARCHES 


Values  of  mL,  rriLX  and  mLy  are  now  computed  for  unit  load  at  each 
load  point  and  tabulated  in  Table  XXIV. 

TABLE  XXIV 


LOAD  AT  A. 

LOAD  AT  B. 

mL 

w 

™Ly 

mL 

mL, 

*• 

1 

1.42 

2.0 

0.0 

2 

4.39 

19.3 

1.0 

3 

7.58 

57.5 

3.8 

4 

11.01 

115.8 

11.1 

1.01 

11.1 

1.0 

5 

14.70 

216.1 

27.8 

4.70 

69.1 

8.9 

6. 

18.67 

348.6 

57.7 

8.67 

161.9 

26.8 

7 

22.94 

526.2 

108.5 

12.94 

296.8 

61.2 

8 

27.50 

756.3 

190.9 

17.50 

481.2 

121.5 

9 

32.35 

1046.5 

318.1 

22.35 

723.0 

219.5 

10 

37.46 

1403.3 

514.0 

27.46 

1028.7 

376.8 

178.02 

4467.9 

1232.9 

94.63 

2770.7 

813.7 

LOAD  AT  C. 

LOAD  AT  D. 

7 

2.94 

67.4 

13.9 

8 

7.50 

206.2 

52.1 

9 

12.35 

399.5 

120.9 

2.35 

76.0 

22.3 

10 

17.46 

644.1 

239.6 

7.46 

269.5 

102.4 

40.25 

1317.2 

426.5 

10.81 

345.5 

124.7 

Substituting  values  from  these  tables  in  Formulas  (12),   (13), 
and  (14),  we  have: 

10X1232. 9-178X42. 0_  .  1   00_ 

—  -p  1 .  ^oO 


Load  at  A. 


4467.  9 


3928 


178.0-2X1.235X42.0 


+3.71 


Load  at  B. 


10X813.7-94.6X42.0 


2770.  7 
Kc~8935.8~ 

,,       94.6-2X1.063X42.0 

—  2Q—  -0. 


Load  at  C. 


OTHER   METHODS  OF  ANALYSIS 
R  =10X426. 5-40. 2X42.0     „ 

1317:2 


317 


Load  at  D. 


=  10X124. 7-10. 8X42.0 
c  3928 

345. 5  _ 
Kc~893O"°^ 

10.8-2X0.20X42.0 
M°  =  -  -20- 


The  thrusts  and  moments  at  any  given  section  of  the  arch  ring, 
due  to  each  load,  may  now  be  found  graphically  (see  Fig.  94).  For 
this  purpose,  draw  the  force  polygon,  laying  off  0— .K=1.0,  the  unit 
load.  From  K,  the  value  of  Vc  is  measured  vertically,  K-v  =  VCy 
for  each  load,  and  Hc  horizontally,  v-A,  v-B,  etc.  The  distance 
Mc/  HC)  measured  vertically  from  the  middle  point  of  the  crown  sec- 
tion, gives  the  point  of  application  of  the  crown  thrust,  k-A,  k-B, 
etc.  The  equilibrium  polygon  in  each  case  consists  of  two  lines  inter- 
secting on  the  line  of  action  of  the  loads  and  parallel  to  the  correspond- 
ing lines  in  the  force  polygon. 

The  thrusts  upon  any  section  of  the  arch  ring  due  to  each  unit 
load  may  now  be  taken  from  the  force  polygon,  while  the  moment  is 
found  by  multiplying  the  value  of  Hc  for  the  given  load  by  the 
vertical  distance  from  the  center  of  section  to  the  equilibrium  polygon. 

Moments  and  thrusts  at  any  section  due  to  dead  or  live  load  at 
each  load  point  may  now  be  found  by  multiplying  the  values  found 
for  unit  load  by  the  amount  of  the  load.  If  these  be  tabulated  and 
combined,  the  maximum  and  minimum  stresses  may  be  obtained. 

176.  Analysis  Using  Arbitrary  Divisions. — The  method  of  analysis 
given  in  Art.  46  requires  that  the  arch  ring  be  so  divided  as  to  make 
s/I  constant  for  all  divisions.  This  simplifies  the  formulas  used  in 
obtaining  values  for  Hc,  Vc,  and  Mc,  but  makes  the  lengths  of  divi- 
sions vary  greatly  where  the  thickness  of  the  arch  ring  increases  from 
crown  to  springing  line,  and  frequently  gives  very  long  divisions  near 
the  ends  of  the  arch,  which  may  sometimes  introduce  considerable 
error  into  the  results. 

A  method  of  analysis  based  upon  the  principle  of  work  in  deflec- 


318  MASONRY  ARCHES 

tion  is  sometimes  employed.  This  is  demonstrated  by  Professor 
Hudson  l  and  is  applied  to  the  analysis  of  the  stresses  in  a  conduit 
by  Professor  French  2  under  the  name  of  the  method  for  indetermi- 
nate structures.  Practically  the  same  formulas  may  be  produced  by 
the  method  of  Art.  46  by  leaving  the  term  s/I  as  a  variable  in  the  for- 
mulas. 

If  the  constant  E  be  eliminated  from  Formulas  (4),  (5),  and  (6) 
of  Section  163,  we  have 

j  and 

Combining  these  with  Equations  (10)  and  (11)  of  the  same  section, 
and  solving  we  find 


O 

2    - 


•    .     .     (33) 


(34) 


Mc=  -  :  -  -  ........     (35) 

'.,..  .          2S7        ||!i  --;' 

In  the  same  manner  for  a  rise  in  temperature,  we  have 


and 


c  /     S\2  S         SJ 


As  an  illustration  of  the  use  of  this  method  of  analysis  we  will 

1  Deflections  and  Statically  Indeterminate  Stresses,  New  York,  1911. 

2  American  Sewage  Practice,  by  Metcalf  and  Eddy,  Vol.  I,  New  York,  1914. 


OTHER  METHODS  OF  ANALYSIS 


319 


compute  the  values  of  Hc,  Vc  and  Mc  for  the  arch  ring  given  in  the 
example  of  Art.  47  with  the  loading  employed  in  Section  168.  Fig. 
95  shows  the  arch  with  divisions  of  equal  length  and  the  loads  upon 


377*  274*294*308*324*332*338*340*341*  342* 


FIG.  95. 

each  division.     Table  XXV  gives  the  coordinates  of  the  centers  of 
divisions,  the  value  of  s/I  for  the  mid-section  of  each  division,  and 

TABLE  XXV— COORDINATES  AND  a/I  FOR  CENTERS  OF  DIVISION 


Points. 

X 

y 

•// 

xs/I 

ys/I 

x*s/I 

y*s/l 

1 

1.71 

0.03 

9.17 

16.26 

0.28 

27.6 

0.00 

2 

5.12 

0.22 

7.90 

40.45 

1.76 

207.0 

0.39 

3 

8.53 

0.62 

6.62 

56.47 

4.10 

481.9 

2.52 

4 

11.92 

1.02 

5.63 

67.10 

5.64 

800.0 

5.85 

5 

15.27 

2.02 

4.83 

73.75 

9.76 

1126.4 

19.70 

6 

18.55 

3.09 

3.62 

67.15 

11.19 

1245.6 

34.57 

7 

21.27 

4.47 

2.62 

57.98 

11.71 

1234.8 

52.40 

8 

24.72 

6.15 

1.86 

45.98 

11.44 

1136.6 

70.35 

9 

27.56 

8.12 

1.30 

35.83 

10.56 

987.7 

85.71 

10 

30.19 

10.35 

0.83 

25.06 

8.59 

756.5 

88.91 

2 

44.72 

75.03 

8004.1 

360.40 

combinations  of  these  quantities  required  in  the  computations. 
Table  XXVI  gives  the  computations  of  the  moments  at  centers  of 
divisions,  and  of  the  terms  in  the  formulas  which  include  these 
moments.  These  computations  might  be  somewhat  shortened  by 
expressing  the  loads  in  Kips  of  1000  pounds  and  the  moments  as 
foot-kips. 


320 


MASONRY  ARCHES 


TABLE  XXVI.— MOMENT  COMPUTATIONS 


TOTAL  LOADS. 

Points. 

Lever 
Arms. 

KIR 

m,L 

s 

(mL+mRf- 

(mL+mR)y~ 

Dead. 

Live. 

1 

0 

0 

0 

0 

0 

0 

0 

0 

2 

1,462 

342 

3.41 

4,985 

6,151 

47,223 

87,974 

19,354 

3 

3,013 

683 

3.41 

15,256 

17,751 

140,967 

218,506 

135,473 

4 

4,665 

1,023 

3.39 

31,069 

36,032 

333,017 

377,778 

385,333 

5 

6,550 

1,361 

3.35 

52,012 

62,534 

777,523 

553,256 

1,117,577 

6 

8,768 

1,693 

3.28 

80,791 

96,866 

1,078,632 

643,118 

1,987,234 

7 

11,325 

2,017 

3.16 

116,578 

139,027 

1,302,042 

669,785 

2,993,939 

8 

14,344 

2,325 

3.01 

159,753 

189,200 

1,354,562 

649,032 

3,993,546 

9 

17,801 

2,619 

2.84 

210,308 

247,193 

1,320,483 

549,751 

4,829,378 

10 

21,856 

2,893 

2.63 

267,789 

312,283 

1,116,799 

481,459 

4,983,100 

2 

7,471,248 

4,274,659 

20,444,934 

Substituting  values  from  the  tables  in  Formulas  (33),  (34),  and 
(35)  we  have, 

20444934  X  44  .  7  -  4274659  X  75 


„ 
H= 


2X360X44. 7-2X(77)2 
7471248 


=  +467  pounds. 

=  +153ft.-lb. 


"2X8004 
4274659-28340X75 


2X44.7 

These  results  are  preferable  to  those  obtained  in  Section  168  on 
account  of  the  better  division  of  the  arch  axis  and  the  inclusion  of 
a  larger  portion  of  the  load  in  the  moments.  The  labor  required  in 
the  use  of  this  method  is  not  materially  greater  than  that  involved 
in  the  use  of  the  ordinary  method  as  given  in  Section  168. 


CHAPTER  XI 

CULVERTS  AND  CONDUITS 
ART.   50.     CULVERTS 

177.  Types  of  Culverts. — The  term  culvert  is  usually  applied 
to  structures  intended  to  provide  small  waterways  through  earth 
embankments.     Such  structures  are  usually  constructed  according 
to  certain  standard  plans,  depending  upon  the  size  of  opening  re- 
quired.    For  the  smaller  openings,  pipe  culverts  of  vitrified  clay, 
plain  or  reinforced  concrete,  cast  iron  or   corrugated  iron,  are  fre- 
quently used. 

For  openings  larger  than  24  or  30  inches  in  diameter,  box  culverts 
or  arch  culverts  of  stone  or  brick  masonry  or  of  concrete,  either  plain 
or  reinforced  are  commonly  employed.  Concrete  for  this  purpose 
has  recently  been  gradually  replacing  the  older  types  of  construction, 
on  account  of  its  ease  of  application  in  most  localities,  and  its  low  cost 
as  compared  with  other  types  of  equal  strength  and  durability. 

Wooden  culverts  have  been  largely  used  in  the  past  upon  highway 
work,  but  are  now  rapidly  giving  way  to  more  permanent  structures, 
for,  while  cheaper  in  first  cost  than  the  other  types,  they  are  very 
uneconomical  on  account  of  their  rapid  deterioration  and  high  cost  of 
maintenance. 

All  culverts  require  walls  of  masonry  or  concrete  at  the  ends  to 
prevent  the  possible  penetration  of  water  around  the  culvert,  and  to 
sustain  the  bank  of  earth  and  hold  it  from  falling  into  and  clogging  the 
waterway.  For  small  culverts,  such  walls  are  usually  parallel  to  the 
roadway ;  they  should  be  long  enough  to  permit  the  earth  to  stand  at 
a  slope  of  about  1  i  to  1  without  reaching  the  waterway  of  the  culvert 
and  sufficiently  high  to  sustain  the  earth  fill  above  the  culvert. 

178.  Area  of  Waterway  Required. — The  waterway  provided  for  a 
culvert  must,  for  safety,  be  sufficiently  large  to  pass  the  maximum  flow 
of  water  that  is  likely  to  occur,  while  for  economy  it  should  be  as 
small  as  possible.     There  are  at  long  intervals,  in  most  localities, 
records  of  storms  of  extraordinary  character,  to  provide  for  which 
would  need  large  increasetof  capacity  in  the  culverts  and  add  greatly 

321 


322  CULVERTS  AND  CONDUITS 

to  their  cost,  and  while  these  unusual  storms  can  hardly  be  taken  into 
account  in  the  design  of  the  structures,  effort  should  be  made  to  pro- 
vide for  any  flow  of  water  that  may  reasonably  be  anticipated.  The 
maximum  flow  of  a  stream  depends  upon  a  number  of  local  conditions, 
most  of  which  are  very  difficult  of  accurate  determination.  Among 
these  are  the  maximum  rate  of  rainfall,  the  area  drained  by  the  stream, 
the  shape  and  character  of  the  surface  drained,  and  the  nature  and 
slope  of  the  culvert  channel. 

The  maximum  rate  of  rainfall  varies  widely  in  different  locali- 
ties, the  heaviest  occurring  over  very  limited  areas  and  short  periods 
of  time,  and  are  therefore  important  only  for  small  culverts.  For 
larger  areas,  the  maximum  rainfall  of  sufficient  duration  to  permit 
water  from  all  parts  of  the  tributary  area  to  reach  the  culvert  gives 
maximum  results. 

The  amount  of  water  reaching  the  culvert  depends  upon  the  per- 
meability of  the  soil,  its  degree  of  saturation,  and  the  amount  of  veg- 
etation. The  rapidity  with  which  water  reaches  the  culvert  from  the 
far  portion  of  the  watershed  depends  upon  the  slope  and  smoothness 
of  the  surface  and  whether  it  is  covered  with  vegetation.  The  shape 
of  the  area  to  be  drained  is  important  in  that  it  determines  the 
distance  the  water  must  travel  in  reaching  the  culvert. 

The  quantity  of  water  which  will  pass  through  a  culvert  in  a  given 
time  depends  upon  the  smoothness  of  its  interior  surface,  the  dis- 
turbance of  flow  at  entrance  to  the  culvert,  and  the  freedom  with 
which  the  water  flows  away  after  passing  the  culvert.  If  the  culvert 
is  so  constructed  that  water  may  stand  against  its  upper  end,  causing 
it  to  discharge  under  pressure,  its  capacity  will  be  considerably 
increased. 

The  determination  of  the  area  of  waterway  required  in  any  in- 
stance is  a  matter  of  judgment,  and  there  is  no  way  in  which  it  may 
be  accurately  computed.  A  number  of  formulas  have  been  pro- 
posed for  the  purpose  of  aiding  in  estimating  the  probable  quantity  of 
water  from  a  given  area  or  the  size  of  opening  required  for  a  given 
area.  The  formula  of  Professor  Talbot  has  been  used  to  consider- 
able extent  in  the  Middle  West  with  good  results.  This  formula  is: 
Area  of  waterway  in  feet  =  C'V/ (drainage  area  in  acres)3,  in  which 
C  is  a  coefficient  depending  upon  local  conditions.  For  rolling 
agricultural  country  subject  to  floods  at  time  of  melting  snow,  and 
with  length  of  valley  three  or  four  times  its  width,  C  =  J.  When  the 
valley  is  longer,  decrease  C.  If  not  affected  by  snow  and  with  greater 
lengths,  C  may  be  taken  at  i,  £,  or  even  less.  For  steep  side  slopes, 
C  should  be  increased.  Where  the  ground  is  steep  and  rocky,  C 


CULVERTS 


323 


may  vary  from  f  to  1.  Table  XXVII  gives  roughly  the  sizes  of 
openings  required  for  different  areas,  computed  from  the  formula 
of  Professor  Talbot. 

TABLE  XXVII.— AREA  IN  SQUARE  FEET  OF  WATERWAY 
REQUIRED 


Area  Drained, 
Acres. 

Steep  Slopes, 
Sq.  Ft. 

Rolling  Agricultural 
Country, 
Sq.  Ft. 

Level  Country, 
Sq.  Ft. 

10 

6 

2 

1 

25 

11 

4 

2 

50 

19 

7 

4 

75 

25 

9 

5 

100 

32 

11 

6 

200 

54 

18 

10 

300 

72 

24 

15 

500 

106 

35 

21 

1000 

180 

60 

35 

For  most  cases  in  practice  the  size  of  waterway  may  be  deter- 
mined from  the  knowledge  which  usually  exists  in  the  vicinity  regard- 
ing the  character  of  a  stream,  from  the  sizes  of  other  openings  upon  the 
same  stream,  or  from  comparison  with  other  streams  of  like  character 
and  extent  in  the  same  locality.  Where  data  of  this  kind  do  not 
exist,  careful  examination  of  water  marks  on  rocks,  the  presence  of 
drift,  etc.,  may  be  made  to  determine  the  height  to  which  water  has 
previously  risen.  The  shape  of  the  valley  and  the  slope  of  the  surface 
is  of  more  importance  than  the  area  of  country  drained.  The  use 
of  a  formula  like  Talbot's  assists  the  arrangement  of  the  factors  which 
enter  into  the  determination,  and  is  intended  only  as  an  aid  to  judg- 
ment in  selecting  the  size  of  opening  required. 

179.  Pipe  Culverts. — Vitrified  clay  pipes  make  satisfactory  as 
well  as  comparatively  cheap  culverts  when  small  openings  are 
required,  and  for  openings  from  12  to  24  inches  in  diameter,  they  may 
often  be  used  economically.  It  is  not  usually  desirable  to  build  a 
culvert  less  than  12  inches  in  diameter.  For  those  larger  than  24 
inches  concrete  will  usually  be  found  more  suitable,  although  vitri- 
fied pipes  30  and  36  inches  in  diameter  are  sometimes  used. 

The  best  quality  of  double-strength,  salt-glazed  sewer  pipe  should 
be  used  for  culverts.  These  pipes  are  made  in  lengths  of  24  and 
30  inches  and  diameter  from  12  to  36  inches,  with  socket  joints. 
They  should  be  sound  and  well  burned,  giving  a  clear  ring  when 
lightly  struck  with  a  hammer. 


324 


CULVERTS  AND  CONDUITS 


The  joints  should  be  filled  with  Portland  cement  mortar  a  require- 
ment particularly  necessary  where  the  pipe  is  likely  to  flow  full,  or 
under  pressure,  as  it  will  prevent  the  water  being  forced  out  and  the 
earth  being  washed  from  around  the  pipe. 

Vitrified  pipes  cannot  safely  be  used  where  they  are  directly 
exposed  to  the  shocks  of  traffic,  and  many  failures  of  such  culverts 
have  been  due  to  this  cause.  In  highway  work  they  should  be  pro- 
tected by  at  least  2  feet  of  filling,  the  roadway  being  graded  so  that  a 
vehicle  may  pass  smoothly  and  without  shock  over  the  culvert.  In 
railway  work  a  fill  of  about  5  feet  over  the  culvert  is  usually  neces- 
sary. The  use  of  vitrified  pipe  for  railway  culverts  is  desirable  only 
under  favorable  conditions,  when  danger  from  shocks  of  traffic  can 
be  avoided,  and  good  foundations  make  breakage  from  settlement 
improbable. 

The  cost  of  vitrified  pipe  varies  widely  with  tne  conditions  of 
trade,  and  with  the  expense  for  freight  and  haulage  to  the  site  of 
the  work.  The  cost  of  laying  the  pipe  depends  upon  local  conditions 
and  the  way  the  work  is  handled.  Table  XXVIII  gives  areas, 
weights,  and  rough  averages  of  costs  in  a  number  of  localities  in  the 
Middle  West  before  the  War. 


TABLE    XXVIII.— APPROXIMATE    DIMENSIONS,     WEIGHTS    AND 
COSTS  OF  VITRIFIED  PIPE  CULVERTS 


Inside  Diameter,  Inches.  .  .          

12 

15 

18 

24 

Area  opening,  square  feet  

0.78 

1.26 

1.76 

3.14 

Weight  of  pipe,  pounds  per  foot  
Cost  of  pipe,  per  foot 

52 

$0  40 

70 
$0.50 

100 
$0.75 

175 

$1.20 

Cost  of  laying,  per  foot 

0  40 

0.60 

0.75 

1.25 

The  ends  of  pipe  culverts  should  always  be  protected  by  a  masonry 
or  concrete  wall.  Fig.  96  shows  a  vitrified  pipe  culvert  with  end 
wall  as  used  in  highway  work.  These  walls  should  extend  at  least  2 
feet  below  the  bottom  of  the  culvert  to  prevent  water  passing  under 
the  culvert  and  undermining  it,  and  should  also  reach  above  the 
surface  of  the  roadway,  thus  serving  as  a  protection  both  to  the  cul- 
vert and  to  the  road.  When  the  culvert  is  under  an  embankment,  the 
wall  should  rise  high  enough  to  catch  the  slope  of  the  embankment 
and  form  a  curb  to  retain  the  earth. 

Table  XXIX  gives  dimensions  that  may  be  used  for  end  walls  for 
highway  culverts  inder  ordinary  conditions. 


CULVERTS 


325 


Culverts  of  cast-iron  pipe  have  been  used  to  considerable  extent 
in  railway  work  for  sizes  from  1  to  4  feet  in  diameter.  The  present 
tendency,  however,  is  to  use  concrete  for  the  larger  openings,  on 


FIG.  96.— Vitrified  Pipe  Culvert. 

account  of  its  relative  cheapness  and  the  occasional  cracking  of  the 
large  iron  pipes.  Ordinary  water  pipe  is  sometimes  used,  but  heavier 
pipe  made  for  the  purpose  is  more  commonly  employed. 

TABLE  XXIX— CONCRETE  END  WALLS  FOR  PIPE  CULVERT 


Diameter  of  Pipe  Inches 

12 

15 

18 

24 

Thickness  of  walls,  inches  

10 

10 

10 

10 

Height  of  walls,  feet,  inches  

5-6 

5-9 

6-0 

6-6 

Length  of  walls,  feet,  inches  

5-0 

6-0 

7-0 

9-0 

Concrete  in  two  walls,  cubic  yards  

1.7 

2.1 

2.5 

3.4 

For  highway  work,  cast-iron  pipe  has  the  advantage  of  resisting 
shocks  better  than  vitrified  pipe,  and  may  be  used  for  small  openings 
where  the  service  is  severe.  It  is  not  extensively  used  on  account  of 
its  cost.  Special  culvert  pipes  in  lengths  of  3  or  4  feet  are  now  avail- 
able, which  are  made  lighter  than  ordinary  water  pipe,  some  of 
them  being  made  with  a  thinner  shell  reinforced  by  ribs.  They  are 
also  made  in  longitudinal  sections  to  be  bolted  together. 

Corrugated  metal  culvert  pipe  is  made  lighter  than  cast  iron,  and 
does  not  ordinarily  differ  greatly  in  price  from  clay  pipe.  It  is 
rather  easy  to  handle  and  is  less  likely  to  break  under  shocks  than 
vitrified  pipe.  It  should,  however,  be  covered  by  a  thickness  of  at 
least  1  foot  of  road  material. 


326 


CULVERTS  AND  CONDUITS 


The  life  of  a  culvert  of  this  kind  depends  upon  the  ability  of 
the  metal  to  resist  rust.  Wrought  iron  is  much  better  than  steel 
in  this  respect,  but  must  be  selected  with  special  reference  to  its 
resisting  qualities.  Pipes  made  of  nearly  pure  iron  have  given  good 
results,  although  numerous  failures  have  resulted  from  the  use  of 
improper  material. 

Concrete  Pipe  Culverts. — Reinforced  concrete  culvert  pipes 
are  sometimes  made  from  18  to  48  inches  in  diameter,  and  in  lengths 
from  4  to  8  feet.  They  usually  have  a  hoop  reinforcement,  as  shown 
in  Fig.  97,  passing  near  the  interior  surface  at  top  and  bottom  and 


FlG.  97. — Concrete  Culvert  Pipe. 

near  the  exterior  surface  at  the  sides,  the  reinforcement  being  bent 
to  circular  form  and  the  pipe  made  in  oval  form  with  the  larger 
diameter  vertical.  Concrete  pipe  is  also  sometimes  made  with  a 
double  reinforcement,  one  line  near  each  surface.  Table  XXX  gives 
dimensions  recommended  by  the  Iowa  State  Highway  Commission 
for  circular  pipe  with  double  reinforcement. 

TABLE  XXX.— CONCRETE  CULVERT  PIPE 


Diameter, 
Inches. 

Thickness  of  Shell, 
Inches. 

Steel  Area  for 
Each  Line, 
Per  Foot  of  Pipe. 

15 

2.25 

.058  in.2 

18 

2.50 

.077  in.2 

24 

3.00 

.102  in.2 

30 

3.50 

.151  in.2 

36 

4.00 

.170  in.2 

42 

4.50 

.225  in.2 

The  load  to  be  carried  by  a  culvert  under  an  embankment  may 
usually  be  taken  as  equal  to  the  weight  of  embankment  immediately 


CULVERTS  327 

above  the  culvert,  and  the  live  load  carried  by  the  roadway  considered 
as  distributed  through  the  fill.  For  pipes  in  trenches  the  weight  of 
filling  is  partly  borne  by  the  sides  of  the  trenches.  A  study  of  pres- 
sures on  pipes  in  trenches  has  been  made  by  Professor  Marston  at 
the  Iowa  State  College,  and  the  very  interesting  results  published  in  a 
bulletin  of  the  Engineering  Experiment  Station  of  the  College. 

A  uniform  horizontal  earth  pressure  over  the  whole  width  of  a 
pipe  produces  positive  bending  moments  at  the  top  and  bottom  sec- 
tions and  negative  moments  at  the  ends  of  the  horizontal  diameter 
which  are  each  equal  to  M  =  Wd/16,  where  W  is  the  total  load  and 
d  the  diameter  of  the  pipe.  The  pipe  must  be  uniformly  supported 
over  its  whole  width  in  this  case.  If  it  is  supported  only  at  the  middle, 
as  when  laid  in  a  flat  trench,  the  moments  at  top  and  bottom  will  be 
about  doubled.  In  laying  pipe  the  bottom  of  the  trench  should  be 
rounded  to  fit  it,  being  cut  a  little  deeper  under  the  middle,  so  that  the 
bottom  is  free,  not  quite  touching  the  soil,  and  letting  the  pipe  rest 
upon  the  soil  at  the  sides.  Depressions  should  also  be  dug  for  the 
sockets  to  prevent  the  pipes  being  supported  at  the  sockets  and  thus 
subjected  to  longitudinal  bending. 

Pipe  should  be  laid  from  the  down  stream  end  with  the  sockets 
upstream.  It  is  also  desirable  to  give  a  slight  crown  to  the  grade  of 
the  culvert  to  provide  for  possible  settlement. 

180.  Box  Culverts. — Rectangular  culverts  are  commonly  used 
for  sizes  too  large  for  pipes.  These  may  be  open  boxes  consisting  of 
a  slab  top  resting  upon  sidewalls,  or  closed  boxes,  in  which  a  bottom 
slab  connects  the  bases  of  the  side  walls  and  distributes  the  load  over 
the  foundation  soil. 

Stone  box  culverts  have  been  extensively  used  in  the  past,  but 
are  now  being  superseded  by  reinforced  concrete;  but  where  suitable 
stone  is  available,  they  may  often  be  found  satisfactory  and  eco- 
nomical. 

The  side  and  end  walls  should  be  built  of  stone  at  least  6  inches 
thick,  laid  in  cement  mortar,  and  with  frequent  headers  extending 
through  the  wall.  The  walls  should  extend  downward  sufficiently 
to  obtain  good  foundations  and  to  be  safe  from  frost.  The  floor  of 
the  culvert  between  the  side  walls  should  be  paved  with  stone,  unless 
it  is  of  material  which  will  resist  erosion. 

The  width  of  opening  for  stone  box  culverts  is  limited  by  the 
dimensions  of  the  cover  stones  available  and  is  never  more  than  4  or 
5  feet.  The  cover  stones  should  have  a  thickness  at  least  one-quarter 
of  the  width  of  opening,  and  should  have  a  bearing  of  about  1  foot 
upon  each  wall. 


328 


CULVERTS  AND  CONDUITS 


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CULVERTS 


329 


Concrete  box  culverts  are  sometimes  constructed  with  a  reinforced 
slab  top  resting  upon  side  walls  which  may  or  may  not  be  reinforced. 
The  design  of  short  bridges  of  this  type  has  been  discussed  in  Chap- 
ter IX.  Where  many  culverts  are  to  be  constructed,  it  is  common  to 
adopt  specific  loadings  and  work  out  standard  forms  and  dimensions 
to  be  used.  Such  standards  have  been  adopted  by  many  railways  and 
State  highway  departments.  Table  XXXI  shows  dimensions  suit- 
able for  ordinary  highway  culverts  5  to  8  feet  in  span,  to  carry  the 
loadings  used  in  Section  156.  The  steel  is  to  be  placed  1J  inches 
from  the  lower  surface  of  the  slab. 

-  Closed  box  culverts  of  reinforced  concrete  are  frequently  used  for 
small   openings,    as    they  I 

require  less  headroom  than 
arched  openings  and  are 
easily  applied  when  open- 
ings are  too  large  for 
convenient  use  of  pipes. 
The  stresses  in  such  a 
culvert  cannot  be  ac- 
curately determined  on 
account  of  the  indeter- 
minate character  of  the 
loads.  A  load  applied  up- 
on the  top  of  the  culvert 
produces  an  equal  upward 
thrust  upon  the  bottom  of  the  culvert,  as  shown  in  Fig.  98,  which 
causes  a  moment  tending  to  bend  the  top  and  bottom  slabs  inward 
and  the  sides  outward. 

Let       6  =  width  of  culvert; 
h  =  height  of  sides; 
w  =  uniform  load  per  foot; 
If  1=  bending  moment  in  top  and  bottom  slabs; 
M 2  =  bending  moment  at  middle  of  sides; 
M 3  =  bending  moment  at  corners; 
1 1  =  moment  of  inertia  of  sections  of  top  and  bottom; 
/2  =  moment  of  inertia  of  sections  of  sides. 

If  we  assume  the  load  to  be  uniformly  distributed  over  the  top, 
the  moments  will  be  as  follows : 

6/37i +h/I2 


1  

1  

a 
r 

—-p*.  ZL<*>_ 

^'4"squore  rod  s,5.5  c-c. 
Alternate  rods  bent  up. 

S'-o" 

-^"square  rods,  if  c-c.          « 
*i 

\  /*"                        ~\  j 

FIG. 


= 
=   8 


and 


6//1+V/2 


330  CULVERTS  AND  CONDUITS 

If  the  sectional  area  of  the  sides  be  made  the  same  as  those  of  the 
top  and  bottom,  we  have 

,,      wtf  b/3+h 


For  a  square  opening  this  becomes 

Mi 
and 


For  sizes  of  culverts  commonly  used  wb2/12  may  be  considered 
the  limiting  value  to  which  the  moment  may  approximate.  The 
moments  in  top  and  bottom  slabs  are  decreased  and  those  in  the 
sides  increased  as  the  ratio  of  height  to  width  is  lessened. 

The  pressure  of  earth  against  the  sides  of  the  culvert  produces 
moments  in  the  top,  bottom  and  sides  of  the  culvert  of  opposite 
sign  to  those  produced  by  the  load  upon  top  of  the  culvert,  and 
therefore  tend  to  reduce  the  effect  of  the  top  load  upon  the  culvert. 
Such  pressures  always  exist  to  some  extent,  but  are  not  accurately 
known.  It  is  usual  to  assume  that  unit  horizontal  pressure,  when 
considered,  is  about  one-third  the  unit  vertical  pressure.  The  mo- 
ments caused  by  the  side  pressures  will  always  be  much  less  than  those 
due  to  the  vertical  loads  and  not  sufficient  to  overcome  those  moments. 

If  the  side  pressures  be  supposed  to  exist  when  the  vertical  loads 
are  not  on  the  culvert,  as  may  be  the  case  with  moving  loads,  the 
sides  will  be  subject  to  positive  moments  and  need  reinforcing  at 
the  inner  surfaces. 

The  existence  of  side  pressures  tends  to  increase  the  negative 
moments  at  the  corners,  and  a  box  culvert  can  act  as  a  whole  only 
when  the  corners  are  reinforced  sufficiently  to  carry  these  moments 
without  cracking  at  the  corners. 

In  case  the  fill  upon  the  culvert  is  not  sufficient  to  distribute  the 
load  over  the  whole  top  of  the  culvert,  the  moment  will  be  increased. 
For  a  concentrated  load  at  the  middle  of  span,  the  moments  will  be 
about  double  those  for  the  same  total  load  distributed  over  the  span. 
In  highway  culverts  which  are  covered  only  with  the  thickness  of 
the  road  surface,  the  distribution  of  the  load  may  be  considered  as 
in  Art.  41.  In  such  culverts,  the  live  load  should  be  increased  25 
per  cent  to  allow  for  impact. 

When,  as  is  sometimes  the  case,  the  corners  of  the  culvert  are  not 
reinforced  for  negative  moment,  the  top  becomes  a  simple  beam, 
resting  upon  the  sides  but  not  rigidly  attached  to  them,  and  the  sides 
carry  only  the  horizontal  earth  pressure  as  simple  beams.  Such 


CULVERTS 


331 


« 


%'  round  bars,  7"c-c. 


^-^  round  bars,  7*c-c. 


9 


FIG.  99. — Section  for  Highway  Culvert. 


construction  is  shown  in  Fig.  99,  which  represents  a  standard  section 
for  a  highway  culvert  de- 
signed to  carry  a  20-ton 
auto  truck.  The  section 
in  Fig.  98  is  designed  for 
the  same  loading. 

181.  Arch  Culverts.— 
For  locations  where  suf- 
ficient headroom  is  avail- 
able, arch  culverts  are 
often  preferable  to  those 
with  flat  top.  Very  pleas- 
ing and  artistic  effects 
may  frequently  be  ob- 
tained by  careful  design 
of  arches  for  such  use.  Under  fills  of  considerable  height,  arch 

culverts  will  commonly  be  more 
economical  to  construct  than 
slab  top  culverts.  Fig.  100 
shows  a  section  for  a  standard 
highway  culvert  for  use  under 
automobile  traffic. 

The  analysis  of  stresses  in 
arch  culverts  may  be  made  in 
the  same  manner  as  is  given  for 
arch    bridges    in    Chapter    X. 
FIG  100  The  horizontal  earth  pressures 

on   the   sides  of  the   arch  are 

usually  taken  as  one-third  of  the  vertical   pressures   at   the   same 
point.     These  pressures  are  of  greater  relative  importance  than  in 


10 


FIG.  101.— Concrete  Barrel  Culvert. 


332  CULVERTS  AND  CONDUITS 

bridges  of  longer  span.  For  short  spans,  plain  concrete  is  com- 
monly employed,  while  for  spans  greater  than  about  8  feet,  rein- 
forcement is  usually  introduced  for  greater  security,  although  not 
necessary  to  carry  moments. 

ART.   51.     CONDUITS 

182.  Types  of  Conduits. — Conduits  for  carrying  water  may  be  de- 
signed either  for  gravity  flow  or  for  internal  pressure.  Brick  masonry 
was  formerly  largely  used  in  the  construction  of  gravity  conduits, 
particularly  for  larger  sewers,  but  is  now  being  replaced  for  the  most 
part  by  the  use  of  concrete.  For  conduits  to  carry  water  under 
pressure,  reinforced  concrete  or  steel  pipe  is  usually  employed. 

A  conduit  consists  essentially  of  two  parts,  the  invert,  which  forms 
the  channel  for  the  water,  and  the  top,  usually  arched,  which  covers 
the  channel  and  carries  the  weight  of  earth  or  other  loads  which  may 
come  upon  it.  The  shape  of  the  invert  depends  upon  the  require- 
ments of  the  service.  In  sewers,  special  forms  of  invert  are  frequently 
needed  to  prevent  deposits  at  times  of  minimum  flow.  The  designs 
of  sections  for  various  uses  may  be  found  in  works  upon  water  supply, 
irrigation,  and  sewerage. 

Sewage  may  sometimes  cause  disintegration  of  concrete,  and  the 
inverts  of  conduits  intended  to  carry  sewage  are  therefore  commonly 
lined  with  vitrified  brick — a  method  particularly  desirable  where  the 
sewage  is  stale  or  impregnated  with  chemicals  from  manufacturing 
plants.  In  conduits  carrying  water  for  irrigation,  injury  to  concrete 
may  result  from  alkalis  in  the  soil  unless  special  precautions  are 
taken. 

The  inverts  of  carefully  constructed  concrete  conduits  usually 
resist  the  abrasion  of  flowing  water  fully  as  well  as  those  with  brick 
or  stone  lining — such  resistance  depending  upon  the  alignment  of 
the  conduit  and  the  amount  of  sediment  carried  by  the  water.  With 
clear  water  and  an  undisturbed  flow,  very  high  velocities  may  pro- 
duce no  appreciable  damage,  while  the  impact  caused  by  changes  in 
the  direction  of  flow  cause  rapid  wear,  particularly  when  sand  and 
gravel  are  carried  by  the  stream. 

No  conduit  is  absolutely  water-tight,  and  careful  attention  should 
always  be  given  to  reducing  leakages  to  a  minimum.  Usually  the 
most  serious  leakage  occurs  at  joints  where  one  section  joins  another, 
although  there  will  generally  be  some  porous  spots  through  which 
small  -quantities  of  water  may  pass.  The  leakage  may  commonly 
be  reduced  to  very  small  proportions  by  careful  design  and  construe- 


CONDUITS 


333 


tion,  reinforcing  so  as  to  prevent  cracks  and  using  dense  and  uniform 
mixtures  of  concrete.  This  subject  is  discussed  in  Art.  23. 

Conduits  of  small  size  are  sometimes  made  rectangular  in  section 
and  designed  in  the  same  manner  as  rectangular  culverts.  Larger 
conduits  are  usually  of  curved  form  with  arched  tops. 

183.  Design  of  Gravity  Conduits. — After  determining  the  size 
and  general  shape  of  conduit  required  for  a  given  service,  the  design 
depends  upon  the  character  of  the  soil  upon  which  it  is  to  be  placed 
and  the  external  loads  that  it  must  carry.  When  the  invert  rests  upon 
a  firm  foundation,  capable  of  supporting  the  structure  without  sen- 
sible yielding,  the  invert  may  be  considered  as  fixed  in  position  and 
the  arch  may  be  designed  with  ends  fixed  upon  the  sides  of  the  invert. 
The  design  of  such  arches  may  be  made  by  the  ordinary  method  used 


Horseshoe  section.  Semi-elliptical  section. 

FIG.  102. — Typical  Sewer  Sections. 

for  arch  bridges  or  culverts.  Actual  loads,  in  so  far  as  they  can  be 
determined,  should  be  used  in  such  designs.  Where  the  loads  are 
light,  such  conduits  may  often  be  built  of  plain  concrete;  usually, 
however,  it  is  preferable  to  reinforce  arches  of  more  than  4  or  5  feet 
span.  Fig.  102  shows  typical  forms  of  standard  sewer  conduits. 

The  horizontal  earth  pressure  to  which  the  side  of  a  conduit  may 
be  exposed  cannot  be  accurately  determined.  It  is  customary  to 
use  Rankine's  minimum  value, 


unit  horizontal  pressure  =  w 


1  —  sin  </> 
l+sin0' 


in  which  w  is  the  unit  vertical  pressure  and  <t>  is  the  angle  of  friction 
of  the  earth.  Taking  0  =  30°  for  ordinary  earth,  this  makes  the  unit 
horizontal  pressure  at  any  point  equal  to  one-third  of  the  unit  vertical 


334 


CULVERTS  AND  CONDUITS 


pressure  at  the  same  point.     In  some  instances  it  may  be  necessary 
to  consider  the  possible  effect  of  variations  in  horizontal  pressures. 


FIG.  103. 


As  the  tendency  of  such  a  structure  under  vertical  loading  is  to  deflect 
outward  upon  the  sides,  it  is  reasonable  to  assume  that  at  least  this 
minimum  horizontal  pressure  may  always  be  depended  upon,  or  a 


CONDUITS 


335 


1 

^2     ^D         O^         ^^         CO         rH         ^^         Ol         *C^         O"l         O^         OJ         C^ 

1 

C^|OOO5COO5t>-l>-OiO5O5O'> 

a 

O 

o                          rH~     co"     TjT     CD"     oo"     cT     o     cT    o" 

PH                                                                                                                    rH         rH         rH         rH 

3 

i 

5 

CO 

Vertical. 

IIIIIIIIIIHI 

rr^ 

_» 

fl    C 

"' 

O    o 

00° 

•3:3 

Is 

^O5iO(NiOCOOO^OiO 
3COC<1OCOI>-I>OO 

0<NCDrHCO*Ol^OC<l 
p^                                   rH          rH          rH          rH          C^          W 

j 

;IZONTAL 

Vertical 
Area. 

*rOOQiOiO*O»OO 
fl;     ^2         O5         ^^         t^»         00         Oi         ^"^         rH 

^r^OrHrHrHrH(N<N 

O 

H 

IS 

COiOioOOC<100O 

Is*          Cft          CO          OO          ^O          rH          t>*          *O 

cocot^-t^-ooososo 

atal  on 
i  vision. 

'giMTtHCOrHOOl^OOCOfNlNiOCq 
Q     ^-ji        ^H        CO        C^        C^l        T^                              'O        ^^        ^^        ^^ 

HQ 

^                                           1     1     1     1 

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"M  ^ 

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4 

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9 

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9 

JN 

ajOOOCOO5I>-COOOO5COcOI> 

r^            ............ 

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^(NrHrHOOOOOrHrHrHrH 

W 

. 

OiOiOOOtO^OOOOOOOOOO 

II 

1      1      1      1 

o 

tiTTVffTT^T? 

e-i.      i>^      i-Aij^-i-^^^T 

3 

336  CULVERTS  AND  CONDUITS 

greater  passive  pressure  if  needed.  In  case  of  soft,  wet  earth,  the 
horizontal  pressure  will  be  much  greater,  reaching  a  maximum  when  it 
is  practically  fluid  and  exerts  normal  pressure  at  all  points. 

Conduits  to  be  supported  upon  compressible  soil  are  often  designed 
to  act  as  a  whole,  assuming  that  all  parts  of  the  structure,  including 
the  invert,  are  equally  subject  to  distortion  under  the  loads.  Fig. 
103  represents  a  half-section  of  a  conduit  of  this  character.  If  we 
assume  the  middle  of  the  invert,  m,  to  be  fixed  in  position,  the  mo- 
ments and  thrusts  in  a  slice  of  the  conduit  1  foot  thick  may  be  found 
in  the  manner  used  for  the  elastic  arch  in  Chapter  X.  The  axis  of  the 
conduit  ring  is  divided  into  lengths  as  shown.  The  lengths  of  the 
divisions,  coordinates  of  the  centers  of  divisions  with  reference  to  the 
crown,  and  thicknesses  of  concrete  at  centers  of  division,  are  given  in 
Table  XXXIII. 

The  loads  given  (Table  XXXII),  are  those  due  to  the  pressure  of 
20  feet  of  earth  above  the  crown  of  the  arch.  The  weight  of  the 
earth  is  taken  at  100  pounds  per  cubic  foot,  and  the  intensity  of  the 
horizontal  earth  pressure  at  one-third  that  of  the  vertical  pressure  at 
the  same  point.  In  computing  the  loads,  the  unit  pressures  at  the 
middle  of  the  extrados  of  the  division  are  considered  as  acting  upon 
areas  equal  to  the  horizontal  and  vertical  projections  of  the  extrados 
of  the  divisions.  The  upward  pressures  upon  the  base  are  considered 
as  acting  vertically  and  uniformly  distributed  horizontally.  The 
computations  of  loads  and  their  moments  about  the  centers  of  divi- 
sion are  shown  in  Table  XXXII. 

The  moment  and  thrust  at  the  crown  section,  a,  may  be  obtained 
by  the  use  of  the  formulas  of  Section  176.  As  the  loading  is  sym- 
metrical about  the  crown,  mL  and  mR  are  equal,  Vc  =  0,  and  Formulas 
(33)  and  (35)  of  Section  176  become 


c 

and 


Table  XXXIII. gives  the  computation  of  the  terms  needed  in 
these  formulas.  As  the  sections  are  rectangular,  no  reinforcement 
being  considered  in  the  computations,  the  value  s/t3  may  be  used 
in  the  formulas  in  place  of  s/I. 


CONDUITS 


337 


gt 

THOCOO»OTtHTtHOOrHTHt>  rJH 

C^O5iOoOOI>CiOOT-iCNiq5  rj< 

Jj  OOlt^-COiOOCOi-HOOOOi-H 

CO        00        CO        »O        ^f 

CO        O^        O^        CO        CQ        00        00        Oi 

00        t^*        O^        ^^        O^        ^O        *O        "^        ^7 

i— ICOrHCOT^T-HlOrHCOCO 

s          £  « 

CO        OO        00        ^^        ^^        CD        t^*        CNI        CP        O^        T-H 

t>-          i-H 

COOCDOOOSOSt^-t^CO 

O 

jSj  C^J^JCOi— (CDOUCDt>.OOOCOCD  !>• 

CD 

,„  4OOIOOOCOCOO5OOOO5OO  CO 

•Bl*«  rHCsqCDCOOOil>COOO'— IT^O  TjH 

T— I 

t^ 

oo 
tl 

00000  rtn' 

888SS2i^g§gg 

^3> 

OOrHCOOCDOOO(M(NCOCO 

« 

^^        C^l        ^^        ^O        CO        CO        CO        CO        ^O        CO        d        ^^ 


? 

4 


338  CULVERTS  AND  CONDUITS 

Substituting  in  the  formulas,  we  have 
„     4841440X14.48-621536X71.43 


617X14.48-(71.43)2 


=6710  pounds. 


Mc    9830 


The  load  diagram  is  now  drawn  as  shown,  and  the  equilibrium 
polygon  (or  line  of  resistance)  constructed,  beginning  with  Hc  at  a 
distance,  e=1.46  feet,  above  the  middle  of  the  crown  section. 

The  thrusts  acting  upon  the  ends  of  divisions  as  found  from  the 
load  diagram  may  be  resolved  into  normal  thrusts  and  shears  as 
shown  by  the  broken  lines.  These  are  tabulated  in  Table  XXXIV. 
The  moments  at  the  centers  of  sections  at  the  end  of  divisions  may  be 
obtained  by  multiplying  the  normal  thrust  upon  the  section  by  the 
distance  from  the  center  of  section  to  the  point  at  which  the  equilib- 
rium polygon  cuts  the  section,  or  they  may  be  computed  by  Formula 
10  of  Section  163,  which  becomes  for  symmetrical  loading 

M  =  Mc+Hcy-m. 

Table  XXXIV,  gives  the  thrusts  and  moments  with  the  resulting 
stresses  at  the  extrados  and  intrados  of  the  sections.  These  results 
show  that  there  are  tensions  at  the  intrados  of  the  crown  section  and 
in  the  invert,  and  at  the  extrados  of  sections  /,  g,  and  h  which  must  be 
cared  for  by  reinforcement.  This  reinforcement  should  be  sufficient 
to  carry  the  tensions  in  the  section  without  materially  changing  the 
position  of  its  neutral  axis.  or  the  compression  upon  the  concrete. 
To  do  this,  the  stress  in  the  steel  should  be  limited  to  about  fifteen 
times  that  shown  for  the  rectangular  section,  or  about  6000  lb./in.2 
at  sections  a  and  g  and  9000  lb./in.2  at  ra.  Computing  the  total 
tension  in  these  sections,  we  find  that  an  area  of  about  2  in.2  of  steel 
per  foot  of  length  is  required  at  a  and  g  and  about  4  in.2  at  ra.  One- 
inch  square  bars  spaced  6  inches  apart  near  the  intrados  at  sections 
a  and  b,  then  crossing  to  the  extrados  at  e  and  extending  along  the 
extrados  to  section  i,  with  If  -inch  square  bars  spaced  6  inches  apart 
near  the  intrados  of  the  invert  would  answer  the  requirement. 

The  maximum  shear  occurs  at  section  j,  the  unit  shear  being  about 
50  lb./in.2,  which  is  not  excessive. 


CONDUITS 


339 


• 

CQ 

°3 
p 

1    . 

i 

^  |  I  a  |  1  §  |  i  §  |  g  8 

0 

i—  iCOC^C^IC^iHT—  I        ^        O        l>        ^ 

1—  1 

lj 

"a"                  »"  a"                      | 

•s| 

"o 

i?7i+  +  +  +  +  +ici'i    i 

-§1 

•^v,  ^i        CO        ^^                    i™^        CO        CO        CO        ^™^        ^^        ^^        *O        CO 

^+    +    +1      1      1       1       1       I4-    +    +    + 

a* 

OOOOCOiOi—  li^OO^OO^OOOOOi 

11 

*| 

OSl^COlMl^C^TtHfrt-COlOrHOiCO 

+  +  +i    17777+^-^ 

11 

0       g       0       0       g       0       g       0       g       g       8       0       g 

coi>-osc<i^cot^ooooosco^^ 

• 

i-ti-iooooooooco'cdoo 
+     +     +II        1        1        1        !+     +     +     + 

Section. 

—  —  —  —  ' 

340  CULVERTS  AND  CONDUITS 

It  seems  probable  that  this  analysis  represents  the  conditions 
giving  the  maximum  stresses  possible  in  the  structure.  For  a  depth 
as  great  as  20  feet,  the  full  pressure  of  the  earth  would  probably  not 
be  borne  by  the  structure.  For  greater  depths,  these  pressures 
need  not  be  increased,  unless  the  earth  is  unstable. 

The  deflection  of  the  conduit  under  the  loads  is  outward  upon  the 
sides,  and,  if  the  earth  is  well  packed  around  the  sides  of  the  conduit 
the  earth  will  resist  that  deflection  and  the  horizontal  earth  pres- 
sures will  probably  be  greater  than  those  used  in  the  analysis.  This 
will  diminish  the  bending  moments  at  all  points  and  reduce  the  need 
for  reinforcement. 

Longitudinal  reinforcement  is  needed  to  prevent  cracking  of  the 
concrete.  Usually  J-inch  bars,  12  inches  apart,  are  sufficient  for 
this  purpose.  Where  the  support  of  the  soil  under  the  conduit  may 
not  be  uniform,  it  is  desirable  to  guard  against  longitudinal  deflection 
by  the  use  of  heavier  reinforcement  near  the  bases  of  the  side  walls. 

187.  Pressure  Conduits. — Conduits  to  carry  water  under  pressure 
are  usually  made  of  circular  or  oval  form.  The  stresses  caused  by 
internal  pressure  are  all  tensile  and  should  be  taken  wholly  by  the 
steel  reinforcement. 

Let    P  =  the  internal  pressure  per  square  inch; 

D  =  the  internal  diameter  of  the  conduit  in  inches; 
/s  =  the  stress  in  the  steel; 
As  =  the  area  of  steel  per  inch  of  length. 

Then  we  have,  As  =  PD/2fs.  Low  values  of  fs  are  desirable  in 
order  to  minimize  the  possibility  of  cracks  in  the  concrete.  Satis- 
factory results  have  been  obtained  in  a  number  of  instances  with 
stresses  from  10,000  to  15,000  pounds  per  square  inch.  The  likeli- 
hood of  cracks  will  be  reduced  by  using  reinforcement  giving  me- 
chanical bond,  such  as  expanded  metal,  diagonal  mesh  or  deformed 
bar,  rather  close  spaced. 

The  thickness  of  concrete,  except  for  small  conduits  under  light 
pressure,  should  be  at  least  6  inches.  When  the  pressure  is  consider- 
able, it  may  be  possible  to  reduce  the  possible  leakage  by  use  of  a 
greater  thickness  with  double  lines  of  reinforcement  and  low  tension 
in  the  steel. 

Pressure  conduits  must  be  capable,  like  gravity  conduits,  of 
carrying  any  exterior  loads  which  may  come  upon  them  when  empty. 
They  may  be  analyzed  in  the  same  manner  as  pipes  or  gravity  con- 
duits for  exterior  loadings. 

Longitudinal  reinforcement  is  required  in  conduits  to  prevent 


CONDUITS  341 

cracking  due  to  changes  in  temperature  and  shrinkage  of  the  concrete. 
When  the  conduit  is  divided  into  sections  by  use  of  expansion  joints, 
light  reinforcement  may  be  sufficient  between  joints,  although  closer 
spacing  is  desirable  than  is  required  for  longitudinal  reinforcement 
in  bridges  or  culverts.  When  prevention  of  leakage  is  important, 
and  the  probable  changes  in  temperature  not  too  great,  continuous 
closely  spaced  longitudinal  reinforcement  may  give  better  results 
than  the  use  of  expansion  joints. 


CHAPTER  XH 

FOUNDATIONS 

ART.   52.    FOUNDATION  MATERIALS 

185.  Examination  of  Soil. — The  stability  of  any  structure  requires 
that  it  be  adequately  supported  by  the  ground  upon  which  it  rests, 
hence  the  nature  of  the  soil  upon  which  the  structure  is  to  be  placed 
is  the  first  subject  for  consideration  in  designing  a  foundation,  and  the 
local  conditions  under  the  surface  of  the  ground  must  be  determined. 
Numerous  instances  might  be  cited  of  the  failure  of  structures  due  to 
lack  of  adequate  investigation  of  soil  conditions,  and  every  effort 
should  be  made  to  obtain  an  accurate  knowledge  of  the  underlying 
strata. 

For  shallow  foundations,  open  excavations  may  be  made  to  a  depth 
somewhat  greater  than  that  of  the  substructure,  which  will  give  the 
advantage  of  permitting  the  examination  of  the  soil  through  and  into 
which  the  substructure  must  be  built  and  observing  its  condition. 
When  the  excavation  is  in  wet  material,  pumping  may  be  required 
to  keep  down  the  water  and  perhaps  sheeting  to  prevent  the  sides 
caving  in — an  expensive  procedure  if  excavating  is  carried  to  con- 
considerable  depth. 

Soundings  are  sometimes  made  with  a  rod,  or  small  pipe  about 
an  inch  in  diameter,  which  is  driven  into  the  ground  with  a  maul. 
When  the  material  near  the  surface  is  soft,  the  depth  to  rock  or  other 
hard  material  may  usually  be  determined  in  this  manner  if  it  is  not 
more  than  20  or  30  feet.  Soundings  serve  to  indicate  whether  resist- 
ance increases  or  decreases,  and  the  depth  at  which  hard  material 
stops  further  progress.  A  number  of  soundings  are  usually  neces- 
sary. A  sunken  log  or  boulder  may  stop  the  rod,  and  mistakes  in 
interpreting  the  results  of  such  soundings  are  easily  made. 

Borings  with  earth  augers  may  be  easily  made  for  small  depths 
with  good  results.  Ordinary  wood  augers  about  2  inches  in  diameter 
have  also  been  used  for  this  purpose,  borings  100  feet  deep  having 
been  made  in  this  manner,  though  for  ordinary  work  to  more  moderate 
depths,  the  use  of  earth  augers  of  larger  diameters  give  better  deter- 

342 


FOUNDATION   MATERIALS  343 

minations.  An  auger  6  inches  in  diameter  may  readily  be  driven  to  a 
depth  of  25  or  30  feet  by  two  men  with  levers.  It  is  held  in  vertical 
position  by  pipes  or  rods  in  sections,  which  may  be  coupled  together 
as  the  hole  becomes  deeper,  and  is  turned  by  hand  with  handles  at  the 
top  2  to  4  feet  long,  which  are  adjustable  in  position  on  the  rods.  The 
auger  is  screwed  into  the  soil  sufficiently  to  fill  it  with  earth,  and  is 
then  brought  to  the  surface  and  the  material  examined,  giving  a  good 
determination  of  the  character  of  the  soil  at  any  depth,  but  not  show- 
ing its  degree  of  compactness.  When  the  hole  passes  through  material 
which  will  not  retain  its  shape,  a  casing  somewhat  larger  than  the 
auger  is  driven,  through  which  the  boring  may  be  done.  When  the 
depth  to  which  the  boring  must  extend  is  considerable,  a  block  and 
fall,  supported  by  a  tripod,  may  be  used  to  draw  the  auger  from  the 
hole. 

Wash  borings  may  be  rapidly  driven  through  soft  soil  or  clay  by 
sinking  a  casing,  with  a  small  pipe  or  hollow  rod  inside  which  carries 
a  jet  of  water  at  its  lower  end.  The  jet  cuts  the  soil  at  the  bottom 
and  brings  up  the  excavated  material  through  the  annular  space 
between  the  jet  pipe  and  casing.  It  is  usual  also  to  have  the  bottom 
of  the  inside  pipe  fitted  with  a  bit  or  chisel,  which  may  aid  in  cutting 
into  hard  material.  Both  jet  pipe  and  casing  are  rotated  as  they 
descend.  When  hard  material  is  met,  it  may  be  necessary  to  cut  it 
with  the  bit  by  churning  the  inside  pipe.  The  bottom  of  the  casing 
is  also  sometimes  flared  slightly  and  fitted  with  teeth  for  cutting. 

When  the  depth  is  not  great  and  only  a  small  amount  of  work  is 
to  be  done,  ordinary  water  pipe  about  2  inches  in  diameter  is  sunk  as 
a  casing,  a  smaller  pipe  f-inch  in  diameter  being  used  inside.  Hand 
appliances  may  be  used  in  handling  these  pipes,  a  tripod  with  block 
and  fall,  levers  for  turning  the  pipes,  and  a  hand  pump  for  applying 
pressure  to  the  jet.  On  more  important  work  hollow  rods  for  holding 
the  jet  and  bits,  special  casings,  and  pipes  with  flush  joints  are 
necessary.  These  may  be  controlled  by  hand,  or  machine  outfits 
similar  to  those  used  in  drilling  wells  may  be  employed. 

Examination  of  the  materials  brought  up  by  the  water  shows  the 
nature  of  the  underlying  strata.  It  does  not,  however,  reveal  the 
moisture  or  compactness  of  the  material.  It  may  therefore  be  desir- 
able to  obtain  cores  of  the  materials  as  they  occur  at  certain  points  in 
the  test  holes,  which  may  be  done  by  substituting  a  cylinder  for  the 
jet  and  bit  upon  the  end  of  the  rod  and  pressing  or  screwing  the  cylin- 
der into  the  soil  at  the  bottom  of  the  hole  until  it  is  filled  with  a 
sample  of  the  material,  which  is  then  drawn  to  the  surface  and 
examined.  This  may  sometimes  prevent  mistakes  in  judging  of 


344  FOUNDATIONS 

subsurface  conditions  where  the  wet  method  of  excavation  is  em- 
ployed. 

Core  drills  are  used  in  testing  rock  strata.  These  consist  of  hollow 
circular  bits,  which  are  rotated  so  as  to  cut  an  annular  channel  into 
the  rock,  leaving  a  circular  core  on  the  inside  of  the  core  barrel  to 
which  the  bit  is  attached.  This  core  is  removed  at  intervals  for 
examination,  and  furnishes  definite  information  concerning  the 
character  of  the  material.  The  core  barrel  is  attached  to  hollow  rods 
through  which  water  may  be  supplied  to  cool  the  bit. 

Several  types  of  bits  are  used  for  this  purpose ;  in  some  the  cutting 
edge  is  formed  of  black  diamonds  or  bort;  in  others,  chilled  shot  are 
used  under  a  hollow  soft  steel  bit;  or  steel  bits  with  teeth  may  be 
employed.  When  diamond  drills  are  used,  the  cores  are  commonly 
from  1  to  2  inches  in  diameter;  the  other  types  are  usually  somewhat 
larger,  varying  from  2  to  4  inches  in  diameter. 

Chopping  bits  are  often  used  in  connection  with  core  drills,  cores 
being  taken  at  intervals  and  the  intermediate  cutting  being  done 
by  the  chopping  drills.  In  any  such  work,  complete  drilling  machines 
are  necessary  and  they  should  be  operated  by  men  experienced  in  the 
work. 

186.  Bearing  Capacity  of  Soils. — Definite  values  of  bearing 
capacity  for  various  soils  cannot  be  stated  with  accuracy,  because 
of  the  variations  in  character  and  condition  of  the  same  kind  of 
soils  and  the  consequent  difficulty  in  classifying  them.  The  ability 
of  the  soil  to  sustain  loads  depends  not  only  upon  its  character,  but 
also  upon  the  amount  of  water  it  contains  and  the  degree  to  which  it 
is  confined  in  position.  The  location  and  drainage  of  the  foundation 
as  well  as  the  character  of  the  soil  must  therefore  be  considered  in 
determining  its  bearing  capacity. 

Solid  rock  makes  the  best  and  most  substantial  foundation,  and 
usually  is  capable  of  carrying  any  load  that  the  masonry  may  bring 
upon  it.  The  loose  and  decayed  portions  of  the  rock  upon  its  surface 
need  to  be  cut  away,  and  the  surface  should  be  trimmed  so  that  there 
will  be  no  tendency  for  the  structure  to  slip  upon  it. 

Clay  soils  vary  widely  in  character.  They  may  be  found  in  any 
condition  from  soft,  wet  clay,  which  will  squeeze  out  laterally  under 
light  pressure,  to  hard,  indurated  clays  capable  of  bearing  heavy 
foundations  without  yielding.  The  supporting  power  is  mainly 
dependent  upon  the  amount  of  moisture  contained  in  the  clay.  The 
tendency  of  clay  to  retain  water  which  it  may  absorb  and  to  soften 
as  the  amount  of  water  increases  is  its  most  important  property. 
Clays  differ  considerably  in  the  readiness  with  which  they  absorb 


FOUNDATION   MATERIALS  345 

water.  Compact,  hard  clays  may  by  proper  drainage  usually  be  kept 
dry  and  capable  of  bearing  heavy  loads,  frequently  8  to  10  tons  per 
square  foot,  while  wet  clay  may  not  safely  carry  more  than  1  ton  per 
square  foot. 

Sand  or  gravel  and  sand  makes  a  good  foundation  when  confined 
laterally  so  that  there  is  no  danger  of  it  being  washed  out,  compact 
gravel  and  sand  being  capable  of  carrying  heavy  loads  without  sen- 
sible settlement.  Water  will  not  soften  it,  and  it  is  but  slightly 
affected  by  frost.  Loads  of  8  or  10  tons  per  square  foot  seem  to  be 
conservative  for  such  material  under  favorable  conditions.  Fine 
sand  when  saturated  becomes  soft  and  mushy  and  is  easily  dis- 
placed; it  must  be  confined  laterally  to  form  a  good  foundation. 
Dry  clean  sand  may  carry  loads  of  2  to  4  tons  per  square  foot,  and 
when  cemented  with  clay  and  protected  from  water  it  may  safely 
carry  loads  of  4  to  6  tons  per  square  foot. 

When  the  top  soil  is  loam  or  made  land,  foundations  should  go 
through  such  materials  to  natural  subsoil  beneath. 

The  thickness  of  the  layer  of  material  in  which  the  foundation  is 
placed  and  the  nature  of  underlying  strata  are  important  factors  in 
determining  the  supporting  power,  as  well  as  the  character  of  the 
foundation  material  itself.  Foundations  in  hard  clay  which  is  soft 
underneath  may  sometimes  safely  carry  1 J  or  2  tons  per  square  foot. 

For  the  foundations  of  buildings,  local  conditions  usually  lead  to 
a  standard  practice,  and  the  building  codes  of  the  various  cities  are 
designed  to  insure  safety  under  the  particular  circumstances  of  each 
place. 

The  depth  of  the  foundation  below  the  surface  of  the  ground  is 
important  in  plastic  material,  the  weight  of  the  earth  being  relied 
upon  to  confine  the  material,  and  prevent  it  squeezing  out  and  lifting 
the  surrounding  area.  Corthell  in  his  "Allowable  Pressure  on  Deep 
Foundations"  has  cited  a  large  number  of  instances  showing  working 
loads  upon  foundations  under  varying  conditions. 

The  pressures  allowed  upon  foundations  by  the  specifications  of 
various  authorities  differ  quite  widely.  The  values  in  Table  XXXV 
represent  the  range  of  maximum  pressures  commonly  given. 

The  character  of  the  structure  to  be  carried  by  a  foundation  may 
frequently  have  an  influence  upon  the  choice  of  a  limiting  value  for 
the  bearing  capacity.  Where  a  slight  settlement  in  the  foundation 
may  be  serious  in  its  effect  upon  the  structure,  very  conservative 
pressures  should  be  adopted. 

187.  Tests  for  Bearing  Capacity. — Direct  tests  of  the  capacity  of 
the  soil  to  support  the  loads  coming  upon  a  foundation  are  frequently 


346 


FOUNDATIONS 


desirable,  they  should  be  supplemental  to  the  examination  of  the 
site  and  cannot  replace  such  examination.  They  are  intended  to  give 
a  more  accurate  idea  of  the  actual  bearing  capacity  than  can  be 
derived  from  observation  of  the  material  upon  which  the  foundation 
is  to  be  placed  and  its  underlying  strata,  and  should  therefore  be 
made  in  the  excavation  at  the  level  upon  which  it  is  proposed  to  place 
the  base  of  the  foundation. 

TABLE  XXXV.— SAFE    BEARING    CAPACITIES    OF    SOILS 


Material, 

Safe  Bearing  Capacity, 
Tons  per  Square  Foot. 

Rock,  limestone  or  sandstone  

15  to  30 

Rock  soft  or  shale 

5  to  10 

Clay,  dry  and  hard,  thick  beds  

4  to    8 

Clay,  moderately  dry  .    . 

2  to    5 

Clay  soft 

1  to    2 

Gravel  and  sand,  well  cemented  

7  to  10 

Gravel,  coarse  

5  to    8 

Sand,  dry  and  well  cemented  .... 

3  to    6 

Alluvial  and  soft  soils 

0  5  to    1 

•  The  methods  of  making  these  tests  vary  considerably.  Some- 
times a  small  area  is  loaded  and  observations  made  of  the  settlement 
under  varying  loads,  from  which  the  probable  safe  bearing  capacity 
may  be  deduced.  In  other  instances,  a  load  of  about  twice  that  pro- 
posed for  the  foundation  is  placed  upon  a  small  area  and  settlement 
for  different  periods  of  time  observed,  with  a  view  to  judging  the 
safety  of  the  proposed  loading.  Usually  a  platform  is  employed  to 
carry  the  load.  The  platform  is  customarily  supported  on  a  pier  of 
about  1  square  foot  area,  or  sometimes  upon  four  legs  at  its  corners. 
The  soil  to  be  tested  is  leveled  to  receive  the  piers  and  provision  made 
for  observing  the  settlement  of  the  base  of  the  pier  under  the  loads. 
The  platform  must  be  so  arranged  as  to  bring  uniform  pressure  upon 
the  area  under  test. 

The  tune  element  is  frequently  a  matter  of  importance,  settle- 
ment in  some  soils  occurring  gradually  during  a  period  of  twenty- 
four  or  forty-eight  hours,  until  a  stable  position  is  reached.  Some 
soils  are  elastic  under  working  loads,  and  the  settlement  diminishes 
as  the  load  is  decreased  after  a  test. 

The  resistance  offered  by  the  soil  to  pressure  upon  a  small  area  is 
not  necessarily  the  same  as  that  which  may  exist  over  a  large  area, 
and  the  results  of  such  tests  must  be  used  very  conservatively  in  the 
design  of  foundations.  These  results,  however,  when  combined  with 


SPREAD  FOUNDATIONS  347 

careful  observations  of  the  character  of  the  materials  underlying 
the  foundation,  give  a  basis  upon  which  to  form  a  judgment  of  safe 
bearing  capacity. 

ART.   53.     SPREAD   FOUNDATIONS 

188.  Distribution  of  Loads. — When  bedrock  is  at  considerable 
depth,  it  frequently  becomes  necessary  to  spread  foundations  over 
large  areas  near  the  surface  of  the  ground  by  the  use  of  footings  at  the 
bases  of  columns  or  walls.  The  method  to  be  employed  in  such  work 
depends  upon  the  area  of  soil  required  to  support  the  loads  and  the 
extent  of  the  footings  necessary  beyond  the  bases  of  the  walls  or 
columns.  When  the  extensions  are  small,  masonry  footings  may 
often  be  employed  to  advantage,  and  this  is  the  most  common  type 
of  foundations  for  light  buildings  upon  firm  soil.  When  footings 
must  extend  to  greater  distances  beyond  the  bases  of  the  walls  or 
piers,  grillage  or  reinforced  concrete  footings  occupy  less  space  and 
are  more  economical. 

In  foundations  of  this  type  some  settlement  is  usually  to  be  ex- 
pected, and  the  object  should  be  to  make  this  settlement  as  small  and 
as  uniform  as  possible.  The  loads  to  be  carried  by  the  different 
parts  of  the  foundation  should  be  ascertained  and  the  footings  so 
proportioned  as  to  bring  uniform  pressure  upon  the  soil  under  the 
foundation.  Inequalities  in  the  settlement  of  the  foundations  of 
buildings  are  apt  to  crack  the  walls,  injuring  the  appearance  when 
not  sufficient  to  impair  the  stability  of  the  structure.  To  pro- 
duce uniform  pressure  it  is  necessary  that  the  center  of  pressure 
of  the  load  pass  through  the  center  of  area  of  the  base  of  the 
foundation. 

In  determining  the  loads  which  may  come  upon  the  footings  in  the 
foundation  of  a  building,  the  dead  loads  and  live  loads  are  separately 
computed.  The  entire  dead  load  is  always  upon  the  foundation, 
while  the  live  load  may  vary,  and  only  such  portion  as  may  reasonably 
be  assumed  usually  to  exist  should  be  used  in  estimating  the  load 
distribution  upon  the  footings,  which  will  depend  upon  the  character 
of  the  building.  In  hotels,  office  buildings,  etc.,  while  the  floors  of 
each  portion  should  be  designed  to  carry  the  maximum  live  load  which 
could  come  upon  it,  only  a  small  percentage  of  the  total  of  this  live 
load  can  reach  the  footings  at  once,  and  it  is  common  to  neglect  it 
altogether.  In  churches,  theaters,  etc.,  the  maximum  floor  loads  are 
more  apt  to  occur,  and  a  larger  percentage  should  be  used  in  design- 
ing the  foundations.  The  building  codes  of  the  various  cities  com- 


348 


FOUNDATIONS 


monly  prescribe  the  loads  to  be  used  in  designing  foundations  for 
buildings. 

When  the  exterior  walls  of  a  building  carry  much  of  its  weight,  the 
center  of  pressure  should  be  somewhat  inside  the  center  of  the  footing, 
thus  avoiding  any  tendency  to  tip  outward  and  crack  the  walls  of 
the  structure;  a  tendency  to  tip  inward  will  be  resisted  by  the  interior 
walls  and  floors.  The  rigid  connection  of  a  lightly  loaded  interior 
wall  with  a  heavily  loaded  exterior  one  often  causes  an  eccentricity 
of  loading  in  the  foundation  which  produces  serious  cracks.  When  a 
series  of  openings  one  above  the  other  through  the  wall  of  a  building 
cause  the  loads  to  be  brought  to  the  foundation  through  piers  between 
the  openings,  the  footings  should  be  disconnected  and  properly  cen- 
tered for  each  pier,  unless  the  foundation  has  sufficient  stiffness  in 
itself  to  distribute  the  loads  over  its  whole  base.  The  walls  of  many 
buildings  are  cracked  over  the  openings  by  the  use  of  continuous 
foundations  in  such  cases. 

189.  Masonry  Footings. — For  light  loads,  footings  of  brick  or 
stone  masonry  or  of  concrete  are  commonly  employed.  Where 

suitable  stone  is  available,  stone 
masonry  is  often  the  most  economi- 
cal, but  concrete  is  now  usually 
preferred.  Brick  footings  are  less 
desirable  on  account  of  the  likeli- 
hood of  the  deterioration  of  the 
bricks  when  used  under  ground. 

In  placing  stone  footings,  the 
stones  must  be  carefully  bedded 
so  as  to  bear  evenly  upon  the 
foundation  soil.  The  projection 
of  the  footing,  when  of  consider- 
able extent,  is  stepped  off  as  shown 
in  Fig.  104.  The  width  of  a  step  should  not  ordinarily  be  greater 
than  two-thirds  of  the  height  of  the  course,  and  a  stone  should  not 
project  more  than  one-third  of  its  length  beyond  the  course  above. 
Footing  stones  under  walls  carrying  heavy  loads  should  be  large  and 
roughly  squared,  and  should  be  set  in  a  thick  bed  of  mortar  to 
give  even  bearing  upon  the  soil  beneath. 

Plain  concrete  footings  are  usually  stepped  off  in  the  same  manner. 
As  the  concrete  footing  is  a  monolithic  structure  and  capable  of 
carrying  small  tensile  stresses,  the  projecting  step  may  be  considered 
as  a  cantilever  carrying  the  upward  thrust  of  the  soil  upon  its  lower 
surface. 


FIG.  104. 


SPREAD  FOUNDATIONS  349 

Let   i  =the  thickness  of  the  footing  at  any  point; 

o  =  the  projection  of  the  footing  beyond  the  point  where  the 

thickness  is  t\ 
p  =  the  pressure  in  pounds  per  square  foot  on  the  bottom  of 

the  footing; 
/  =  unit  stress  upon  the  concrete  due  to  bending. 

Then  the  allowable  projection  for  any  given  thickness  is 


Thus,  if  we  assume  the  safe  tension  on  the  concrete  to  be  60  lb./in.2, 
and  the  pressure  upon  the  foundation  soil  as  2  tons  per  square  foot, 
o  =  .85tj  or  the  projection  should  not  be  greater  than  .85  of  its  thick- 
ness. 

The  projections  for  cut  stone  in  which  each  stone  is  the  full  height 
of  the  course  may  be  estimated  by  the  above  formula,  provided  the 
stones  may  be  considered  as  firmly  held  in  place  under  the  wall. 
When  placed  upon  compressible  soil,  however,  the  pressure  will  not 
be  uniformly  distributed  over  the  base  of  the  stone,  and  there  is  like- 
lihood of  tipping  the  block  if  the  projection  is  too  great. 

Under  brick  walls,  a  bed  of  concrete  is  usually  employed  at  the 
base  and  the  brickwork  stepped  off  on  top  of  this  to  give  the  required 
extensions.  The  offsets  in  such  work  should  not  be  more  than  three- 
quarters  of  their  heights,  which  may  be  composed  of  two  courses  of 
brick. 

190.  Grillage  Foundations.  —  When  a  foundation  must  be  spread 
over  an  area  which  is  large  compared  to  that  of  the  column  or  wall 
resting  upon  it,  a  masonry  footing  becomes  uneconomical  and  a  foot- 
ing possessing  greater  transverse  strength  and  requiring  less  height 
becomes  desirable.  For  such  foundations,  grillages  of  timber  or 
steel  or  reinforced  concrete  slabs  are  commonly  employed. 

Steel  I-beam  grillages  are  now  very  frequently  used  under  heavy 
buildings.  The  construction  of  foundations  of  this  type  was  begun 
in  Chicago  about  1880.  In  founding  heavy  buildings  upon  the  clay 
subsoil,  it  was  necessary  to  spread  the  footings  over  considerable 
areas,  and  room  was  not  available  for  masonry  footings,  as  the  sub- 
soil was  soft  at  greater  depths.  A  footing  consisting  of  several  layers 
of  old  steel  rails  encased  in  concrete  was  devised  and  used  for  some 
time.  This  was  soon  replaced  by  I-beams  of  sufficient  depth  to 
carry  the  loads  in  a  single  layer,  thus  saving  space  and  giving  better 
economy  in  the  use  of  the  metal. 

A  grillage  footing  as  applied  to  the  foundation  of  a  single  column  is 


350 


FOUNDATIONS 


shown  in  Fig.  105. 


Such  foundations  rest  upon  a  bed  of  concrete 

, and  are  enclosed  by  a  filling  and 

surfacing  of  concrete  for  the  pro- 
tection of  the  steel.  Under  heavy 
loads,  the  bed  of  concrete  is 
usually  about  12  inches  thick  and 
the  protective  coating  from  3  to 
6  inches  thick.  The  beams 
should  be  held  by  spacers  at  least 
3  inches  apart  in  the  clear  in 
order  to  permit  filling  the  spaces 
with  concrete.  Under  a  contin- 
uous wall,  a  block  of  plain  con- 
crete is  usually  employed  instead 
of  the  upper  series  of  I-beams. 

In  designing  a  grillage  footing, 
the  loads  to  be   carried  and  the 

^^^^^^^^^^^^^^^^^^       areas   of   the  walls  or   piers  are 
ji|  |?r    known  and  the  grillage  must  be 

•  »••••"-•••  •^••-. •.•;•••  ••.v^"  •*.*'•'.•••:**•'•''•'••'•?  .-•••** •'•••••vv-'f    so  placed  as  to  bring  the  center  of 
FIG.  105.  its  area  in  the  line  of  action  of  the 

resultant  load.     The  total  load 

may  be  considered  as  distributed  uniformly  over  the  base,  giving 
uniform  upward   pressure  upon  the  beams,    while   the   downward 


<-2.75-»r* 


10.5 


4.25 


3000  OO I  b. 


r   F 


400000. 1  b. 


2.5 


3     -* 


FIG.  106. 


SPREAD  FOUNDATIONS  351 

thrust  of  a  pier  is  taken  as  uniformly  distributed  over  its  section. 
Usually  a  grillage  is  centered  under  each  column  or  wall,  proportioned 
to  the  load  to  be  carried,  bat  two  or  more  loads  may  be  carried  by  a 
single  grillage  when  it  seems  desirable. 

Fig.  106  shows  a  footing  supporting  two  piers  each  2.5  feet  square, 
one  carrying  a  load  of  300,000  pounds  and  the  other  400,000  pounds, 
spaced  10.5  feet  between  centers.  The  soil  pressure  is  limited  to 
4000  lb./ft.2  and  an  area  of  175  ft.2  is  required.  If  this  area  be 
assumed  as  17.5  feet  by  10  feet  as  the  center  of  gravity  of  the  loads  is 
4.5  feet  from  the  center  of  the  pier  carrying  the  larger  load,  the  piers 
will  occupy  the  positions  shown,  when  the  pressure  is  uniform  upon 
the  soil. 

The  upper  tier  of  beams  under  the  heavier  load  carries  400,000 
pounds  distributed  over  2.5  feet  at  the  middle  acting  downward  on  its 
upper  surface,  and  the  same  load  distributed  uniformly  over  the 
length  of  10  feet,  acting  upward  on  its  lower  surface.  The  maximum 
moment  will  be  at  the  mid-section  and  will  be 

M  =  200000  X  5/2  -  200000  X  .625  =  375000  Ib.-f t. 
If  the  allowable  unit  stress  in  the  steel  is  16,000  lb./in.2, 

7/6  =  375000X12/16000  =  281  in.2,  and  we  might  use 

2— 24-in.  80  Ib.  I-beams,  I/e  173.9  each,  flange  7  in.  wide 
2— 20-in.  80  Ib.  I-beams,  I/e  146.6  each,  flange  7  in.  wide 
3— 18-in.  60  Ib.  I-beams,  I/e  93.5  each,  flange  6.1  in.  wide 

The  20-inch  beams  require  less  concrete  than  the  24-inch,  and  less 
steel  than  the  18-inch  and  may  be  used,  although  the  spacing  is 
rather  wide.  The  flanges  are  spaced  10  inches  apart  and  3  inches 
inside  the  block  of  concrete. 

Under  the  load  of  300,000  pounds,  I/e  should  be  210  in.3,  and 
two  20-inch  65-pound  I-beams  may  be  used. 

The  lower  tier  of  beams  carries  two  loads  of  400,000  and  300,000 
pounds  respectively,  acting  downward  upon  its  upper  surface,  each 
distributed  over  2.5  feet  as  shown,  and  a  load  of  4000  pounds  per 
square  foot  uniformly  distributed  over  its  lower  surface.  There 
are  sections  of  maximum  moment  under  each  load  and  at  some  point 
between  them.  These  sections  are  where  the  shear  passes  through 
zero.  Let  y  =  distance  from  end  of  beam  to  section.  Under  the 
heavier  load,  the  shear  is 


352  FOUNDATIONS 

-3)=0,  and2/=4. 


Then 

Ib.-ft. 


For  the  mid-section,  4000  XKty-  400,  000  =  0,  and  y  =  W. 
Then 

M  =  4000X10X10X10/2-400000(10-4.25)  =  -300000  Ib.-ft. 

The  greatest  moment  is  300,000  Ib.-ft.  or  3,600,000  lb.-in.,  and  the 
required  I/e  is  3,600,000/16,000  =  225  in.2 

Eleven  6-in.  12.25-pound  I-beams,  7/e  =  21.8  each,  flange  3.33 
inches  wide,  clearance  8.4  inches  may  be  used.  Three  or  four 
additional  beams  may  be  introduced  if  thought  desirable  to  reduce 
the  clearance.  If  this  is  not  done,  light  transverse  reinforcement 
might  be  placed  in  the  concrete  covering  the  beams. 

The  moments  might  be  somewhat  decreased  and  the  positive  and 
negative  moments  made  more  nearly  equal  by  making  the  foundation 
narrower  upon  the  end  carrying  the  smaller  load  and  widening  the 
other  end.  The  same  steel  area  would  then  be  needed  at  both  ends 
and  the  spaces  between  the  beams  would  widen  from  one  end  to  the 
other. 

It  may  frequently  be  convenient  to  carry  three  or  more  piers  or 
columns  upon  one  grillage.  In  such  a  design,  the  line  of  action  of  the 
resultant  of  all  the  loads  must  pass  through  the  center  of  area  of  the 
grillage.  Two  loads  are  usually  carried  upon  one  set  of  the  upper  tier 
of  beams,  which  is  arranged  to  give  uniform  loading  to  the  tier  below 
at  right  angles  to  it. 

Timber  grillages  may  be  employed  where  the  footing  is  so  located 
as  to  be  continually  wet.  They  are  also  commonly  used  for  tem- 
porary footings  which  are  to  be  removed  in  a  comparatively  short 
time.  These  foundations  are  usually  constructed  by  placing  a 
layer  of  2-inch  planks  on  the  bed  to  be  occupied  by  the  footing  and 
across  these  one  or  more  series  of  timbers  in  the  same  manner  that 
the  I-beams  are  used  in  the  steel  grillages.  The  timbers  must  be 
capable  of  carrying  the  bending  moments  due  to  transmitting  the 
loads  from  the  walls  or  piers  to  the  soil  upon  which  the  footing  rests. 
On  top  of  the  grillage  a  floor,  usually  of  3-inch  plank,  is  placed  to 
carry  the  base  of  the  masonry.  All  timber  in  such  foundations  must 
be  kept  below  low  water  and  the  spaces  between  the  timbers  should 
be  filled  with  sand  or  broken  stone. 

191.  Reinforced  Concrete  Footings.  —  Reinforced  concrete  slabs 


SPREAD  FOUNDATIONS 


353 


are  ordinarily  used  as  footings  for  the  distribution  of  loads  in  spread 
foundations.  When  used  under  walls,  these  consist  of  a  cantilever 
projecting  on  each  side  of  the  wall;  the  determination  of  thickness  and 
amount  of  reinforcement  is  made  as  for  a  simple  cantilever.  When 
used  under  columns  or  piers,  the  load  may  be  transmitted  to  the  slab 
through  beams,  or  flat  slabs  with  two-way  or  four-way  reinforcement 
may  be  employed. 

When  beams  are  used,  the  moments  may  be  computed  by  the 
methods  used  for  I-beam  grillages  and  reinforced  concrete  beams  and 
slabs  with  one-way  reinforcement  designed  to  resist  these  moments  in 
the  usual  manner.  If  the  construction  is  monolithic,  the  maximum 
stresses  occur  in  the  sections  where  the  slabs  join  the  beams  and  in 
the  beams  where  they  join  the  base  of  the  pier.  The  stresses  in 
such  foundations  may  be  ac- 
curately computed  in  so  far  as 
the  loads  are  known,  and  they 
are  not  subject  to  the  assump- 
tions required  in  the  flat-slab 
computations.  Usually  these 
footings  are  cheaper  in  cost  of 
materials  than  flat-slab  foot- 
ings, but  require  more  form 
work  in  construction. 

In  a  flat-slab  footing  with 
two-way  reinforcement,  the 
maximum  moment  in  the  slab 
occurs  in  the  sections  through 
the  face  of  the  pier.  In  the 
footing  shown  in  Fig.  107,  it 
is  assumed  that  the  section 
through  each  face  carries  the 
moment  between  that  face  and 
the  side  of  the  footing.  Thus, 
the  moment  of  the  upward 
pressures  on  the  area  A  BCD 

is  supposed  to  be  borne  by  the  section  C-D.  These  moments 
are  not  uniformly  distributed  over  the  section,  but  must  be 
greater  in  the  portion  between  C  and  D  than  in  its  ends.  From 
experiments  made  at  the  University  of  Illinois,  Professor  Talbot 1 
concludes  that  "For  footings  having  projections  of  ordinary  dimen- 
sions, the  critical  section  for  the  bending  moment  for  one  direction 
1  Bulletin  No.  67,  Engineering  Experiment  Station,  Univ.  of  111. 


B 


FIG.  107. 


354  FOUNDATIONS 

(which  in  two-way  reinforced  concrete  footings  is  to  be  resisted  by  one 
set  of  bars)  may  be  taken  to  be  at  a  vertical  section  passing  through 
the  face  of  the  pier.  In  calculating  this  moment,  all  the  upward 
load  on  the  rectangle  lying  between  a  face  of  the  pier  and  the  edge  of 
the  footing  is  considered  to  act  at  a  center  of  pressure  located  at  a 
point  halfway  out  from  the  pier,  and  half  of  the  upward  load  on  the 
two  corner  squares  is  considered  to  act  at  a  center  of  pressure  located 
at  a  point  six-tenths  of  the  width  of  the  projection  from  the  given 
section. 

"With  two-way  reinforcement  evenly  spaced  over  the  footing,  it 
seems  that  the  tensile  stress  is  approximately  the  same  in  bars  lying 
within  a  space  somewhat  greater  than  the  width  of  the  pier  and  that 
there  is  also  considerable  stress  in  the  bars  which  lie  near  the  edges  of 
the  footing.  For  intermediate  bars,  stresses  intermediate  in  amount 
will  be  developed.  For  footings  having  two-way  reinforcement 
spaced  uniformly  over  the  footing,  the  method  proposed,  for  deter- 
mining the  maximum  tensile  stress  in  the  reinforcing  bars,  is  to  use  in 
the  calculation  of  resisting  moment  at  a  section  at  the  face  of  the 
pier  the  area  of  all  the  bars  which  lie  within  a  width  of  footing  equal 
to  the  width  of  pier  plus  twice  the  thickness  of  footing,  plus  half  the 
remaining  distance  on  each  side  to  the  edge  of  the  footing.  This 
method  gives  results  in  keeping  with  the  results  of  tests.  When  the 
spacing  through  the  middle  of  the  width  of  the  footing  is  closer,  or 
even  when  the  bars  are  concentrated  in  the  middle  portion,  the  same 
method  may  be  applied  without  serious  error.  Enough  reinforcement 
should  be  placed  in  the  outer  portion  to  prevent  the  concentration 
of  tension  cracks  in  the  concrete  and  to  provide  for  other  distribution 
stresses. 

"The  method  for  calculating  maximum  bond  stress  in  column 
footings  having  two-way  reinforcement  evenly  spaced,  or  spaced 
as  noted  in  the  preceding  paragraph,  is  to  use  the  ordinary  bond-stress 
formula,  and  to  consider  the  circumference  of  all  the  bars  which  were 
used  in  the  calculation  of  tensile  stress,  and  to  take  for  the  external 
shear  that  amount  of  upward  pressure  or  load  which  was  used  in  the 
calculation  of  the  bending  moment  at  the  given  section." 

Example. — A  column  2  feet  square  is  to  carry  a  load  of  300,000 
pounds  on  soil  that  may  safely  carry  3000  pounds  per  square  foot. 
It  is  required  to  design  a  square  footing  with  two-way  reinforcement, 
using  concrete  of  2000  pounds  compressive  strength  and  unit  stress 
of  16,000  lb./in.2  upon  the  steel. 

The  required  area  of  footing  is  300000/3000  =  100  square  feet.  A 
base  10  feet  square  will  be  used. 


SPREAD  FOUNDATIONS  355 

The  thickness  of  footing  required  for  shear  at  base  of  column  is 
300000-4X3000 


4X24X120 


=  25  inches. 


Using  Talbot's  rule,  the  moment  of  the  load  upon  DCEF  (Fig. 
107)  is  2X4X3000X2X12  =  576000  in.-lb.;  that  of  the  loads  DFB 
and  ACE  is  4X4X3000X2.4X12=  1382400  in.-lb. 

Total,  M  =  576000  +  1382400  =1958400  in.-lb. 

The  effective  width  of  section  is  2+2.1X2+1.9  =  8.0  feet. 

The  depth  required  for  moment  is  (Formula  (9)  Chapter  VI) 


If  we  use  the  depth  of  25  inches, 

Jf=          1958400  2 

*    fsjd     16000 X. 875X25 

Nineteen  f-inch  bars  in  the  width  of  8  feet  gives  an  area  of  5.8  in.2 
and  a  spacing  of  about  5  inches.  Four  additional  bars  or  23  in  all 
should  be  used  in  the  full  width  of  10  feet. 

The  maximum  shear  is  equal  to  the  load  upon  the  area  ABDC, 

300000-4X3000 

— j—        —  =  72000  pounds, 

and  the  bond  stress  is 

V  72000 

=  S^=19X1.96X.875X25  = 

This  is  rather  high  for  plain  bars,  but  deformed  bars  may  be  used. 

According  to  Talbot's  rules,  the  shear  for  diagonal  tension  may 
be  computed  on  a  section  distant  the  depth  of  footing  from  the  base 
of  the  pier,  which  will  give  a  shear 

F  =  [(10)2-(2+2X2.1)2]3000  =  184680  pounds, 
and  a  unit  shear 

v=184680/[4(24-2x25)X.875X25]  =  291b./in.2 
and  no  diagonal  tension  reinforcement  is  necessary. 

The  volume  of  concrete  in  the  above  footing  may  be  decreased  by 
widening  the  base  of  the  pier  or  placing  a  block  of  concrete  under  it 
as  shown  in  Fig.  108.  If  a  step  6  inches  wide  be  used,  making  the 
block  3  feet  square,  the  depth  of  footing  required  is  found  to  be  16 


356 


FOUNDATIONS 


inches.  Reinforcement  for  diagonal  tension  would  be  required 
for  this  depth  but  by  increasing  it  to  17  inches,  the  shear  may  be  so 
reduced  as  to  make  this  unnecessary.  This  change  would  decrease 
the  volume  of  concrete  required  by  about  30  per  cent  and  increase 
the  weight  of  steel  by  20  to  25  per  cent. 

Four-way  Reinforcement. — When  a  four-way  reinforcement  is 
used,  each  set  of  bars  is  supposed  to  carry  an  equal  share  of  the  mo- 
ment. As  the  length  of  the  diagonal  bars  are  not  the  same  as  those 
parallel  to  the  sides  of  the  footing,  this  supposition  is  only  approxi- 


JL2. 


jl 


B 


FIG.  108. 


FIG.  109. 


mately  correct,  but  in  the  absence  of  more  definite  information  con- 
cerning the  distribution  of  stress  it  may  be  used  in  design. 

If  a  four-way  reinforcement  be  used  in  the  example  already 
given,  as  shown  in  Fig.  109,  the  depth  required  for  shear  at  the 
base  of  the  pier  will  be  as  before ,  25  inches.  The  moment  of  the 
upward  thrust  upon  the  area  A  BCD  about  the  section  CD  is,  as 
before,  1,958,400  in.-lb.  If  the  width  of  section  be  supposed  to 
carry  all  of  the  compression  due  to  this  moment,  the  depth  of  section 
required  will  be 


108X24 


=  28  inches. 


SPREAD  FOUNDATIONS  357 

The  depth  to  the  steel  will  be  made  28  inches  at  the  base  of  the  pier 
and  slope  to  6  inches  at  the  edges  of  the  slab,  thus  giving  greater 
depth  than  necessary  at  all  intermediate  points. 

~  M  ___         1958400  2 

s    fsjd     16000  X.  875X28 


Sixteen  ^e-inch  square  bars  may  be  used.  The  maximum  bond 
stress  will  be 

V  72000  _7A1K/-     2 

"Z5&"16X2.5X.  875X28" 

Eight  bars  will  be  placed  parallel  to  the  edge  of  the  footing  and 
eight  on  the  diagonal  in  each  direction;  they  may  cover  a  greater 
width  than  the  base  of  the  pier,  and  will  be  spaced  5  inches  apart, 
thus  making  each  band  3  feet  wide  and  covering  the  whole  area  in 
a  satisfactory  manner. 

The  method  for  diagonal  tension  in  a  slab  of  this  form  has  not 
been  satisfactorily  worked  out.  If  we  apply  the  method  proposed 
by  Professor  Talbot  for  slabs  with  flat-top  surface,  we  have,  on  a 
section  distant  28  inches  from  the  base  of  the  pier, 

V  =  [(10)2  -  (6.67)2]3000  =  166600  pounds, 
and 

166600  Qn  „    /.    2 

y=4X80X.  875X15.  2  =  39  lb'/m'  ' 

and  no  diagonal  tension  reinforcement  is  necessary.  As  the  section 
to  resist  diagonal  tension  is  increased  by  the  slope  of  the  top  surface 
of  the  beam,  it  seems  reasonable  to  employ  the  [method  in  this 
instance. 

Various  modifications  of  these  forms  of  footing  are  often  employed, 
depending  upon  the  same  principles  in  design,  but  varied  to  suit 
special  needs  or  to  secure  greater  economy  in  the  use  of  materials. 
Ribs  may  sometimes  be  used  to  advantage  in  distributing  the  loads 
upon  the  slab. 

Cantilever  Foundations.  —  When  it  is  necessary  to  carry  the  side 
walls  or  wall  columns  of  buildings  upon  footings  which  cannot  pro- 
ject beyond  the  face  of  the  wall  on  the  outside,  cantilever  footings 
are  often  employed,  wherein  the  wall  columns  rest  upon  one  arm  of  a 
cantilever  beam,  the  other  arm  of  which  carries  an  interior  column, 
the  cantilever  being  so  proportioned  as  to  center  the  total  load  upon 
the  footing  which  supports  it.  Footings  of  this  type  are  often  neces- 
sary when  the  loads  upon  the  wall  columns  are  greater  than  those 
upon  the  interior  column,  so  that  the  ordinary  combined  footing  is 


360  FOUNDATIONS 

in  placing  it  in  position  and  to  raise  and  lower  the  hammer  in  driving. 
The  leads  are  supported  in  position  by  a  triangular  framework  braced 
with  backstays.  The  platform  or  deck  to  which  the  framework  is 
attached  also  carries  a  hoisting  engine  with  friction  drums  for  han- 
dling the  pile  and  hammer  lines.  The  general  arrangement  is  shown  in 
Fig.  111.  The  details  of  arrangement  and  method  of  mounting  vary 
widely  according  to  the  service  for  which  the  machine  is  intended. 

Pile-drivers  may  be  so  mounted  as  to  move  forward,  backward, 
and  to  the  side  by  the  use  of  rollers,  or  made  to  turn  in  any  direction 
by  mounting  upon  a  turntable.  For  river  work,  they  are  usually 
rigidly  connected  to  the  deck  of  a  barge  which  is  moved  to  place  the 
driver  in  position. 

For  railway  work,  drivers  are  commonly  mounted  upon  cars,  and 
many  of  them  are  very  carefully  designed  to  render  efficient  service 
under  varying  conditions.  The  cars  are  made  self-propelling  to 
make  the  machine  independent  of  locomotive  service,  and  leads  which 
can  be  quickly  raised  and  lowered  are  employed.  The  drivers  are 
mounted  upon  turntables  which  permit  driving  upon  either  side, 
and  the  leads  are  arranged  so  that  they  may  be  turned  to  an  inclined 
position  for  the  purpose  of  driving  batter  piles.  The  stability  of 
the  machines  when  driving  at  the  greatest  reach  from  the  cars  is  im- 
portant and  must  be  carefully  considered  in  design.  Combina- 
tion machines,  in  which  service  as  pile  drivers  is  added  to  that  as 
derricks  or  as  excavators  are  also  frequently  employed. 

A  drop-hammer,  as  used  in  driving  piles,  usually  consists  of  a  solid 
casting,  which  is  raised  by  means  of  a  rope  and  allowed  to  drop  upon 
the  head  of  the  pile.  The  hammer  slides  in  guides  upon  the  leads  and 
should  be  so  shaped  as  to  give  it  a  low  center  of  gravity  and  a  sufficient 
length  to  cause  it  to  slide  in  the  guides  without  rocking;  it  may  be 
given  a  free  fall  by  the  use  of  nippers  which  engage  a  pin  upon  the 
hammer  and  are  automatically  disengaged  at  a  certain  height  upon 
the  leads.  The  more  common  method,  however,  is  to  raise  and  drop 
the  hammer  by  the  use  of  a  hoisting  drum  with  a  friction  clutch,  the 
rope  being  permanently  attached  to  the  hammer — a  more  rapid 
system,  which  permits  the  operator  to  regulate  readily  the  height  of 
fall.  The  weight  of  hammer  employed  in  ordinary  work  varies  from 
about  2000  to  3500  pounds.  For  light  work  in  small  operations,  light 
hammers  may  be  used,  while  for  heavy  service  and  unusual  conditions, 
heavier  ones  may  be  necessary.  A  heavy  hammer  with  low  fall  is 
more  effective  in  driving  than  a  light  hammer  with  high  fall,  as  it 
may  be  operated  more  rapidly  and  causes  less  vibration  in  the  ma- 
chine. 


PILE   FOUNDATIONS  361 

A  steam  pile-hammer  is  one  which  is  raised  and  dropped  by  a  steam 
piston  working  in  a  cylinder  attached  to  a  frame  which  rests  upon  the 
head  of  the  pile.  The  frame  slides  in  the  guides  upon  the  leads,  and 
the  striking  part  or  hammer  is  guided  by  the  frame.  In  some  of  the 
steam  hammers  the  pistons  are  attached  to  the  striking  weight;  in 
others,  the  cylinders  are  the  moving  parts. 

Steam  pile-hammers  are  of  two  types — single  acting,  in  which  the 
weight  is  raised  by  the  steam  pressure  and  allowed  to  drop  by  gravity; 
double  acting,  in  which  the  steam  pressure  is  used  to  accelerate  the 
downward  motion  of  the  hammer  and  increase  the  force  of  the  blow. 
Single-acting  hammers  are  made  heavier  and  of  longer  stroke  than 
double-acting  ones  for  the  same  service,  and  are  slower  in  action. 
For  heavy  service,  single-acting  hammers  usually  have  strokes  of 
36  to  42  inches  and  strike  50  to  70  blows  per  minute,  while  the  double 
acting  kind  have  strokes  from  12  to  24  inches  and  strike  120  to  200 
blows  per  minute.  Lighter  machines  may  work  much  faster. 

The  blows  of  the  steam  hammer  are  so  rapidly  given  that  the 
motion  of  the  pile  is  practically  continuous  and  under  many  conditions 
the  effectiveness  of  the  driving  is  thereby  greatly  increased.  There 
are  few  data  giving  definite  information  concerning  the  relative  costs 
of  driving  by  drop-hammer  or  steam-hammer,  but  the  steam-hammer 
has  seemed  to  be  gradually  replacing  the  drop-hammer  in  important 
operations.  It  has  "as  advantages  that  of  causing  less  damage  to  the 
head  of  the  pile;  the  driving  may  be  accomplished  at  a  more  rapid 
rate,  and  more  piles  may  usually  be  driven  in  the  same  time;  the  wear 
and  tear  upon  the  machine  is  much  less  than  in  the  use  of  the  drop- 
hammer,  although  the  first  cost  of  the  steam-hammer  is  consider- 
ably greater. 

Water-jet  pile  drivers  are  fitted  with  appliances  for  discharging  a 
jet  of  water  at  the  foot  of  the  pile.  The  water  comes  up  around  the 
pile,  bringing  with  it  much  of  the  material  cut  from  beneath  the  pile 
and  lessening  the  friction  resisting  its  descent.  The  water-jet  equip- 
ment is  usually  a  straight  piece  of  pipe,  which  may  be  held  alongside 
the  pile,  with  a  nozzle  at  its  lower  end,  the  upper  end  being  con- 
nected by  a  flexible  hose  to  a  pump  which  supplies  water  under  pres- 
sure. The  driver  is  equipped  with  leads  and  hammer,  the  latter  being 
used  to  assist  in  sinking  the  pile  by  light  blows  and  to  settle  it  firmly 
into  place  after  the  jet  is  stopped. 

The  water  jet  is  especially  applicable  to  driving  piles  into  sand, 
which  usually  offers  considerable  resistance  to  driving  by  the  hammer 
alone.  It  may  be  used  in  any  material  which  will  be  washed  up  by 
the  jet  and  puddled  about  the  pile,  and  frequently  effects  large  savings 


360  FOUNDATIONS 

in  placing  it  in  position  and  to  raise  and  lower  the  hammer  in  driving. 
The  leads  are  supported  in  position  by  a  triangular  framework  braced 
with  backstays.  The  platform  or  deck  to  which  the  framework  is 
attached  also  carries  a  hoisting  engine  with  friction  drums  for  han- 
dling the  pile  and  hammer  lines.  The  general  arrangement  is  shown  in 
Fig.  111.  The  details  of  arrangement  and  method  of  mounting  vary 
widely  according  to  the  service  for  which  the  machine  is  intended. 

Pile-drivers  may  be  so  mounted  as  to  move  forward,  backward, 
and  to  the  side  by  the  use  of  rollers,  or  made  to  turn  in  any  direction 
by  mounting  upon  a  turntable.  For  river  work,  they  are  usually 
rigidly  connected  to  the  deck  of  a  barge  which  is  moved  to  place  the 
driver  in  position. 

For  railway  work,  drivers  are  commonly  mounted  upon  cars,  and 
many  of  them  are  very  carefully  designed  to  render  efficient  service 
under  varying  conditions.  The  cars  are  made  self-propelling  to 
make  the  machine  independent  of  locomotive  service,  and  leads  which 
can  be  quickly  raised  and  lowered  are  employed.  The  drivers  are 
mounted  upon  turntables  which  permit  driving  upon  either  side, 
and  the  leads  are  arranged  so  that  they  may  be  turned  to  an  inclined 
position  for  the  purpose  of  driving  batter  piles.  The  stability  of 
the  machines  when  driving  at  the  greatest  reach  from  the  cars  is  im- 
portant and  must  be  carefully  considered  in  design.  Combina- 
tion machines,  in  which  service  as  pile  drivers  is  added  to  that  as 
derricks  or  as  excavators  are  also  frequently  employed. 

A  drop-hammer,  as  used  in  driving  piles,  usually  consists  of  a  solid 
casting,  which  is  raised  by  means  of  a  rope  and  allowed  to  drop  upon 
the  head  of  the  pile.  The  hammer  slides  in  guides  upon  the  leads  and 
should  be  so  shaped  as  to  give  it  a  low  center  of  gravity  and  a  sufficient 
length  to  cause  it  to  slide  in  the  guides  without  rocking;  it  may  be 
given  a  free  fall  by  the  use  of  nippers  which  engage  a  pin  upon  the 
hammer  and  are  automatically  disengaged  at  a  certain  height  upon 
the  leads.  The  more  common  method,  however,  is  to  raise  and  drop 
the  hammer  by  the  use  of  a  hoisting  drum  with  a  friction  clutch,  the 
rope  being  permanently  attached  to  the  hammer — a  more  rapid 
system,  which  permits  the  operator  to  regulate  readily  the  height  of 
fall.  The  weight  of  hammer  employed  in  ordinary  work  varies  from 
about  2000  to  3500  pounds.  For  light  work  in  small  operations,  light 
hammers  may  be  used,  while  for  heavy  service  and  unusual  conditions, 
heavier  ones  may  be  necessary.  A  heavy  hammer  with  low  fall  is 
more  effective  in  driving  than  a  light  hammer  with  high  fall,  as  it 
may  be  operated  more  rapidly  and  causes  less  vibration  in  the  ma- 
chine. 


PILE   FOUNDATIONS  361 

A  steam  pile-hammer  is  one  which  is  raised  and  dropped  by  a  steam 
piston  working  in  a  cylinder  attached  to  a  frame  which  rests  upon  the 
head  of  the  pile.  The  frame  slides  in  the  guides  upon  the  leads,  and 
the  striking  part  or  hammer  is  guided  by  the  frame.  In  some  of  the 
steam  hammers  the  pistons  are  attached  to  the  striking  weight;  in 
others,  the  cylinders  are  the  moving  parts. 

Steam  pile-hammers  are  of  two  types — single  acting,  in  which  the 
weight  is  raised  by  the  steam  pressure  and  allowed  to  drop  by  gravity; 
double  acting,  in  which  the  steam  pressure  is  used  to  accelerate  the 
downward  motion  of  the  hammer  and  increase  the  force  of  the  blow. 
Single-acting  hammers  are  made  heavier  and  of  longer  stroke  than 
double-acting  ones  for  the  same  service,  and  are  slower  in  action. 
For  heavy  service,  single-acting  hammers  usually  have  strokes  of 
36  to  42  inches  and  strike  50  to  70  blows  per  minute,  while  the  double 
acting  kind  have  strokes  from  12  to  24  inches  and  strike  120  to  200 
blows  per  minute.  Lighter  machines  may  work  much  faster. 

The  blows  of  the  steam  hammer  are  so  rapidly  given  that  the 
motion  of  the  pile  is  practically  continuous  and  under  many  conditions 
the  effectiveness  of  the  driving  is  thereby  greatly  increased.  There 
are  few  data  giving  definite  information  concerning  the  relative  costs 
of  driving  by  drop-hammer  or  steam-hammer,  but  the  steam-hammer 
has  seemed  to  be  gradually  replacing  the  drop-hammer  in  important 
operations.  It  has  as  advantages  that  of  causing  less  damage  to  the 
head  of  the  pile;  the  driving  may  be  accomplished  at  a  more  rapid 
rate,  and  more  piles  may  usually  be  driven  in  the  same  time;  the  wear 
and  tear  upon  the  machine  is  much  less  than  in  the  use  of  the  drop- 
hammer,  although  the  first  cost  of  the  steam-hammer  is  consider- 
ably greater. 

Water-jet  pile  drivers  are  fitted  with  appliances  for  discharging  a 
jet  of  water  at  the  foot  of  the  pile.  The  water  comes  up  around  the 
pile,  bringing  with  it  much  of  the  material  cut  from  beneath  the  pile 
and  lessening  the  friction  resisting  its  descent.  The  water-jet  equip- 
ment is  usually  a  straight  piece  of  pipe,  which  may  be  held  alongside 
the  pile,  with  a  nozzle  at  its  lower  end,  the  upper  end  being  con- 
nected by  a  flexible  hose  to  a  pump  which  supplies  water  under  pres- 
sure. The  driver  is  equipped  with  leads  and  hammer,  the  latter  being 
used  to  assist  in  sinking  the  pile  by  light  blows  and  to  settle  it  firmly 
into  place  after  the  jet  is  stopped. 

The  water  jet  is  especially  applicable  to  driving  piles  into  sand, 
which  usually  offers  considerable  resistance  to  driving  by  the  hammer 
alone.  It  may  be  used  in  any  material  which  will  be  washed  up  by 
the  jet  and  puddled  about  the  pile,  and  frequently  effects  large  savings 


362  FOUNDATIONS 

in  costs  of  driving.  The  pressure  and  volume  of  water  required 
depend  upon  the  kind  of  material  to  be  penetrated.  The  pressure 
must  be  sufficient  to  cut  the  material  and  the  volume  enough  to 
bring  it  up  alongside  the  pile.  Pressures  of  75  to  150  lb./in.2  and 
volumes  from  about  50  to  200  gallons  per  minute  are  common. 

194.  Timber  Piles. — A  timber  pile  is  usually  the  lower  portion  of 
the  trunk  of  a  tree,  from  which  the  branches  and  bark  have  been 
removed.  It  is  nearly  circular  in  section  and  tapers  from  butt  to 
tip.  Many  kinds  of  timber  are  employed  for  the  purpose.  The  coni- 
fers— yellow  pine,  Douglas  fir,  spruce,  and  cedar — are  commonly 
obtainable  in  straight  pieces  of  considerable  length.  White  and  post- 
oak  piles  are  not  so  straight,  but  are  tough  and  hard  and  are  suitable 
when  requirements  are  severe.  Cedar  is  valuable  on  account  of  its 
durability.  For  ordinary  work  in  foundations,  piles  are  usually 
required  to  be  not  less  than  6  inches  in  diameter  at  the  top,  and 
commonly  vary  from  10  to  18  inches  at  the  butt. 

The  specifications  of  the  American  Railway  Engineering  Associa- 
tion name  the  following  requirements  for  timber  piles: 

RAILROAD  HEART  GRADE 

1.  This  grade  includes  white,  burr,  and  post  oak;    longleaf  pine,  Douglas 
fir,  tamarack,  Eastern  white  and  red  cedar,  chestnut,  Western   cedar,  redwood 
and  cypress. 

2.  Piles  shall  be  cut  from  sound  trees;   shall  be  close-grained  and  solid,  free 
from  defects,  such  as  injurious  ring  shakes,  large  and  unsound  or  loose  knots, 
decay  or  other  defects,  which  may  materially  impair  their  strength  or  durability. 
In  Eastern  red  or  white  cedar  a  small  amount  of  heart  rot  at  the  butt,  which 
does  not  materially  injure  the  strength  of  the  pile,  will  be  allowed. 

3.  Piles  must  be  butt  cut  above  the  ground  swell  and  have  a  uniform  taper 
from  butt  to  tip.     Short  bends  will  not  be  allowed.     A  line  drawn  from  the  center 
of  the  butt  to  the  center  of  the  tip  shall  lie  within  the  body  of  the  pile. 

4.  Unless  otherwise  allowed,  piles  must  be  cut  when  sap  is  down.     Piles  must 
be  peeled  soon  after  cutting.     All  knots  shall  be  trimmed  close  to  the  body  of 
the  pile. 

5.  The  minimum  diameter  at  the  tips  of  round  piles   shall  be  9   inches  for 
lengths  not  exceeding  30  feet;    8  inches  over  30  feet  but  not   exceeding  50  feet 
and  7  inches  for  lengths  over  50  feet.     The  minimum  diameter  at  one-quarter 
of  the  length  from  the  butt  shall  be  12  inches  and  the  maximum  diameter  at  the 
butt  20  inches. 

6.  The  minimum  width  of  any  side  of  the  tip  of  a  square  pile  shall  be  9  inches 
for  lengths  not  exceeding  30  feet;  8  inches  for  lengths  over  30  but  not  exceeding 
50  feet,  and  7  inches  for  lengths  over  50  feet.     The  minimum  width  of  any  side 
at  one-quarter  of  the  length  from  the  butt  shall  be  12  inches. 

7.  Square  piles  shall  show  at  least  80  per  cent  heart  on  each  side  at  any  cross- 
section  of  the  stick,  and  all  round  piles  shall  show  at  least  10  §  inches  diameter 
of  heart  at  the  butt. 


PILE  FOUNDATIONS  363 

RAILROAD  FALSEWORK  GRADE 

8.  This  grade  includes  red  and  all  other  oaks  not  included  in  Railroad  heart 
grade,  sycamore,  sweet,  black  and  tupelo  gum,  maple,  elm,  hickory,  Norway 
pine,  or  any  sound  timber  that  will  stand  driving. 

9.  The  requirements  for  size  of  tip  and  butt,  taper  and  lateral  curvature  are 
the  same  as  for  Railroad  heart  grade. 

10.  Unless  otherwise  specified  piles  need  not  be  peeled. 

11.  No  limits  are  specified  as  to  the  diameter  or  proportion  of  heart. 

12.  Piles  which  meet  the  requirements  of  Railroad  heart  grade  except  the  pro- 
portion of  heart  specified  will  be  classed  as  Railroad  Falsework  grade. 

Piles  are  driven  with  the  tips  down,  although  in  some  instances 
it  is  desirable  to  drive  the  butts  down.  In  certain  soils,  as  quicksand, 
the  upward  pressure  on  the  sides  of  the  piles  may  force  the  pile  up- 
ward after  being  driven  with  the  tip  down.  Where  piles  are  being 
driven  through  soft  material  to  a  hard  substratum,  it  may  be  desir- 
able to  drive  them  with  the  butts  down  in  order  to  obtain  larger  bear- 
ing surface  at  the  base. 

The  butt  of  the  pile  is  cut  off  accurately  at  a  right  angle  to  its 
length  in  order  that  the  blow  of  the  hammer  may  be  uniformly  dis- 
tributed over  the  section.  When  the  hammer  strikes  directly  upon 
the  head  of  the  pile,  it  is  common  to  use  a  hammer  with  a  slightly 
concave  upper  surface.  This  tends  to  keep  the  pile  centered  in  the 
leads,  and  minimizes  the  brooming  effect  of  the  blow.  Heavy  blows 
upon  the  head  of  a  pile  have  a  tendency  to  splinter  and  broom  it,  and 
a  portion  of  the  energy  of  the  blow  is  used  up  in  injury  to  the  pile. 
When  the  brooming  effect  has  become  considerable,  the  efficiency  of 
the  driving  is  greatly  decreased,  and  a  large  portion  of  the  work 
is  wasted.  It  has  frequently  been  observed  that  when  the  broomed 
head  of  a  pile  has  been  cut  off,  an  increase  in  the  penetration  under 
each  blow  is  obtained,  the  penetration  being  in  some  cases  more 
than  doubled. 

Pile  rings  are  frequently  placed  upon  the  heads  of  piles  to  reduce 
the  brooming  effects.  They  are  made  of  wrought  iron  from  2  to  4 
inches  wide  and  |  to  1  inch  thick;  the  pile  is  chamfered  off  so  that  the 
ring  may  be  started  on  and  be  driven  into  place  by  the  hammer. 
The  rings  are  used  repeatedly  and  serve  for  a  larger  number  of  piles. 

Pile  caps  consisting  of  cast-iron  blocks  with  tapered  recesses  above 
and  below  are  used  for  the  same  purpose.  The  head  of  the  pile  is 
fitted  into  the  lower  recess  and  a  hard-wood  block  into  the  upper  one. 
The  block  is  reinforced  by  a  ring  at  the  top  and  receives  the  blow  of 
the  hammer.  The  cap  fits  into  the  guides  of  the  leads,  and  holds 
the  head  of  the  pile  in  place.  After  the  pile  is  in  place,  the  cap  is 
drawn  from  its  head  by  being  attached  to  the  hammer.  Some  steam 


364  FOUNDATIONS 

hammers  are  provided  with  anvils,  which  rest  upon  the  head  of  the 
pile  and  receive  the  blow  of  the  hammer. 

In  driving  piles  through  hard  material,  it  is  often  desirable  to 
point  the  lower  end,  by  cutting  the  end  of  the  pile  in  the  form  of  a 
pyramid,  a  blunt  end  3  or  4  inches  square  being  left  at  the  bottom. 
A  thinner  point  is  apt  to  be  too  easily  injured. 

When  piles  are  needed  of  greater  length  than  those  available,  it 
becomes  necessary  to  splice  two  piles  together,  which  is  accomplished 
by  the  use  of  fish  plates.  The  ends  of  the  two  piles  are  cut  square  and 
butted  together,  the  sides  are  trimmed  flat  for  a  considerable  distance 
on  each  side  of  the  splice  and  long  wooden  fish-plates  are  spiked  to 
the  sides,  four  or  six  fish-plates  being  commonly  used. 

194.  Bearing  Power  of  Piles. — There  are  so  many  variable  factors 
affecting  the  supporting  power  of  pile  foundations  that  in  most  in- 
stances accurate  determinations  are  not  possible.  Piles  may  derive 
their  support  either  from  a  hard  stratum  at  the  bottom  which  resists 
the  penetration  of  the  foot  of  the  pile,  or  from  friction  of  the  sides 
of  the  pile  upon  the  material  through  which  it  is  driven.  Conditions 
may  also  vary  widely  as  to  the  lateral  support  afforded  the  pile  be- 
tween the  loaded  end  and  the  point  of  support. 

Piles  Acting  as  Columns. — When  piles  are  driven  through  soft  soil, 
offering  slight  resistance  to  lateral  motion,  and  rest  upon  a  hard 
substratum  below,  they  may  be  considered  as  columns.  They  are 
fixed  in  position  at  the  bottom  with  the  top  free  to  move  laterally  but 
held  in  vertical  position  by  the  caps  joining  them  together.  Piles 
driven  in  water  and  not  braced  depend  for  lateral  stiffness  upon 
being  driven  into  the  soil  beneath  to  a  sufficient  depth  to  hold  them 
firmly  at  the  bottom.  The  length  of  the  column  in  such  a  pile  is  to 
be  taken  from  the  cap  to  a  point  below  the  surface  of  the  soil,  a 
distance  depending  upon  the  firmness  of  the  soil.  In  stiff  soil  a 
depth  of  1  or  2  feet  may  be  sufficient  to  firmly  hold  the  pile.  In  less 
resistant  soils,  one-third  to  one-half  the  total  penetration  may  be 
required. 

When  piles  project  into  the  air,  they  are  braced  laterally,  so  that 
no  bending  can  take  place  and  the  strength  of  the  pile  is  that  of  the 
compressive  strength  of  the  wood,  or  the  resistance  to  penetration  of 
the  soil  into  which  it  is  driven.  The  compressive  resistance  of 
wooden  piles  depends  upon  the  kind  of  wood  employed,  but  is  taken 
at  a  low  value,  commonly  about  600  lb./in.2  When  the  pile  acts  as 
a  column,  this  is  reduced  to  600(l-L/60d),  in  which  L  is  the  length 
of  the  column  and  d  is  the  diameter  at  its  middle  point. 


PILE  FOUNDATIONS  365 

Piles  Supported  by  Friction. — Numerous  attempts  have  been  made 
to  state  in  a  formula  the  relation  between  the  penetration  of  a  pile 
under  a  hammer  blow  of  given  energy  and  the  load  the  pile  may  bear 
without  yielding.  The  effective  work  done  upon  the  pile  by  the 
hammer  in  striking  the  blow  should  equal  the  work  done  by  the 
resistances  in  stopping  penetration.  There  are,  however,  so  many 
indeterminate  losses  of  energy  in  the  operation  of  striking  the  blow 
that  a  rational  formula  is  not  feasible — there  is  loss  of  energy  in  the 
friction  of  the  hammer  in  the  guides;  some  energy  is  consumed  in 
brooming  the  head  of  the  pile;  the  elastic  compression  of  the  pile 
consumes  a  part  of  the  energy;  the  effectiveness  of  the  blow  is  affected 
by  the  height  of  fall  and  velocity  of  the  hammer.  The  impossibility 
of  evaluating  these  and  other  data  affecting  the  resulting  penetration 
renders  any  formula  obtained  by  discussion  of  the  theory  of  the  subject 
rather  useless.  Mr.  Ernest  P.  Goodrich  has  made  a  very  elaborate 
and  interesting  study  1  of  the  subject  in  which  is  produced  a  formula 
of  very  complicated  form.  This  formula  is  reduced  by  evaluating 
experimentally  many  of  the  terms,  but  the  result  seems  to  show  that 
a  usable  rational  formula  cannot  be  produced. 

Engineering  News  Formula. — This  formula  was  suggested  in  1888 
by  Mr.  A.  M.  Wellington,  the  editor  of  Engineering  News.  When  the 
drop-hammer  is  used  this  formula  is  P=2Wh/(s-l),  in  which  P  is  the 
safe  load  in  pounds,  W  is  the  weight  of  the  hammer,  h  is  the  height  of 
fall  in  feet,  and  s  the  average  penetration  under  the  last  blows  in 
inches.  When  using  a  steam  hammer  the  formula  suggested  by 
Mr.  Wellington  is  P  =  2Wh/(s-Q.l). 

These  formulas  are  the  only  ones  in  common  use.  They  are  em- 
pirical formulas  obtained  by  studying  all  available  data  derived  from 
tests  of  bearing  power.  It  is  assumed  that  the  blows  have  been 
struck  upon  sound  wood  and  commonly  it  may  be  necessary  to  cut 
off  the  head  of  the  pile  to  remove  the  wood  splintered  or  broomed  by 
previous  driving  before  making  the  tests.  There  must  be  no  visible 
rebound  of  the  hammer  in  striking  the  blows,  and  if  such  rebound 
occurs,  it  indicates  that  the  fall  is  too  great  or  the  hammer  too  light, 
and  the  full  effect  of  the  blow  is  not  communicated  to  the  pile.  The 
hammer  must  always  be  heavier  than  the  pile,  and  should  be  twice 
as  heavy,  in  order  to  strike  an  effective  blow.  The  formulas  are 
supposed  to  give  a  factor  of  safety  of  about  six. 

Bytdwein's  formula  is  frequently  used  for  reinforced  concrete 
piles,  on  account  of  the  greater  weight  of  such  piles.  This  formula 
1  Transactions,  Am.  Soc.  C.  E.,  Vol.  XLVIII,  p.  180. 


366  FOUNDATIONS 

takes  into  account  the  relative  weights  of  pile  and  hammer.     With  a 
factor  of  safety  of  six  the  formula  is 

,  ,   ,  2WhH 

Safe  load 


s(l-WP/Wh) 

in  which  Wh  is  the  weight  of  hammer,  Wp  the  weight  of  pile,  H  the 
height  of  fall  and  s  the  penetration. 

It  is  desirable  that  the  blows  used  for  measuring  penetration  be 
struck  with  a  hammer  having  free  fall,  as  considerable  loss  of  velocity 
may  result  from  the  resistance  of  a  rope  and  friction  drum.  It  is  also 
necessary  that  the  penetration  under  the  last  few  blows  be  uniform 
and  fairly  represent  the  state  of  resistance  of  the  pile.  The  penetra- 
tion should  not  be  less  than  one-half  inch,  as  less  penetration  may 
indicate  injury  to  the  pile  rather  than  resistance  to  penetration. 

When  piles  are  driven  into  soft  or  plastic  materials,  the  resistance 
to  penetration  usually  increases  with  time  after  the  driving  ceases. 
A  rest  of  twenty-four  hours  may  be  sufficient  to  cause  the  material 
to  settle  against  the  surface  of  the  pile  so  as  to  develop  a  resistance 
several  tunes  that  existing  when  the  material  was  disturbed  by  the 
operation  of  driving.  Numerous  instances  are  recorded  in  which  it 
was  found  that  the  penetration  under  a  blow  had  been  decreased  by  a 
rest  of  a  few  days  to  from  one-third  to  one-sixth  of  that  at  the  end  of 
the  original  driving.  In  case  of  driving  into  material  of  this  kind,  it 
is  desirable  to  examine  the  effect  of  rest  upon  the  bearing  power  and 
piles  upon  which  tests  are  to  be  made  should  have  a  period  of  rest 
before  the  final  test  is  made.  Piles  easily  sunk  by  light  blows  or  even 
by  static  pressure  frequently  carry  loads  a  few  days  later  much  greater 
than  those  required  to  sink  them.  In  coarse  sand  or  gravel,  the  time 
effect  is  of  less  importance,  if  it  exists  at  all. 

Piles  are  frequently  tested  by  applying  static  loads  until  movement 
occurs.  Usually  a  load  is  balanced  over  a  single  pile,  although  some- 
times a  platform  resting  upon  several  piles  is  loaded.  The  pile  is 
allowed  to  stand  under  the  load  at  least  twenty-four  hours  before 
being  examined  for  settlement.  It  is  desirable  that  the  load  be  added 
in  increments,  each  being  allowed  to  stand  for  twenty-four  hours, 
until  a  load  is  obtained  which  produces  settlement. 

In  any  test  of  bearing  power,  it  is  essential  that  the  pile  be  tested 
under  the  same  conditions  that  will  afterward  apply  to  the  foundation. 
The  determination  of  the  requirements  in  any  particular  instance  is 
largely  a  matter  of  judgment  on  the  part  of  the  engineer,  but  such 
judgment  should  be  exercised  with  knowledge  of  all  conditions  that 


PILE  FOUNDATIONS  367 

may  be  evaluated  and  in  accordance  with  the  principles  underlying 
such  work. 

The  spacing  of  piles  in  a  foundation  is  a  matter  of  importance 
because  of  its  possible  bearing  upon  the  supporting  power  of  the 
individual  piles.  In  general,  piles  should  not  be  closer  than  3  feet 
center  to  center,  although  they  are  sometimes  driven  2£  feet  apart. 
When  piles  are  closely  spaced  over  the  area  of  a  foundation,  a  consid- 
erable compression  of  the  soil  between  them  must  result.  The  effect 
of  this  disturbance  of  the  soil  depends  upon  its  character,  but  too  close 
driving  impairs  the  bearing  capacity  of  all  of  the  piles,  and  they  can- 
not be  considered  as  individually  carrying  loads  up  to  their  normal 
bearing  capacity. 

196.  Concrete  Piles. — Timber  piles  in  structures  intended  to 
be  permanent  must  be  cut  off  below  the  water  line,  while  concrete 
may  be  used  without  reference  to  moisture  conditions.  In  many 
instances,  therefore,  the  use  of  concrete  piles  is  more  satisfactory  and 
economical  than  that  of  wood,  sometimes  effecting  large  savings  in 
excavation.  They  may  be  made  in  any  size  considered  desirable  and 
are  not  subject  to  the  limitations  of  wooden  piles  in  this  respect. 

Concrete  piles  may  be  either  molded  in  place  or  molded  before 
placing  and  then  driven  like  wooden  piles.  Those  molded  in  place 
are  generally  not  reinforced,  while  those  to  be  driven  after  molding 
must  be  reinforced  so  as  to  resist  the  stresses  brought  upon  them  in 
handling  and  driving.  The  methods  employed  for  molding  piles  in 
place  are  patented,  and  a  number  of  forms  of  pre-molded  piles  are 
also  patented. 

The  Raymond  pile  is  made  by  driving  into  the  ground  a  thin  shell 
of  sheet  steel  with  a  collapsible  core  which  holds  the  shell  to  its  form 
while  driving.  When  the  shell  has  been  driven  to  the  required  pene- 
tration, the  core  is  withdrawn  and  the  shell  filled  with  concrete. 
It  is  made  tapering,  usually  18  to  20  inches  in  diameter  at  the  head 
and  6  to  8  inches  at  the  foot,  with  a  closed  boot  of  heavier  steel. 
They  are  made  in  sections  for  convenience  in  shipping. 

The  taper  adopted  for  these  piles  gives  high  bearing  capacity  under 
ordinary  conditions  of  use.  The  interior  of  the  form  may  be  in- 
spected before  placing  the  concrete.  Difficulty  is  sometimes  met  in 
the  collapsing  of  the  thin  shell  when  heavy  hydrostatic  pressure  comes 
upon  it,  a  fault  sometimes  corrected  by  driving  a  second  shell  inside 
the  first  one. 

The  Simplex  pile  is  formed  by  driving  into  the  ground  a  heavy 
steel  pipe  with  the  bottom  closed  by  a  special  jaw.  The  pipe  is 
driven  to  the  depth  required,  and  is  then  withdrawn  as  the  hole  is 


368 


FOUNDATIONS 


filled  with  concrete.  The  jaw  opens  as  the  pipe  is  raised,  permitting 
the  concrete  to  pass  through,  and  the  concrete  is  rammed  into  place 
so  as  to  fill  completely  the  hole  below  the  end  of  the  pipe,  and  press 
the  concrete  against  the  earth  at  the  sides  of  the  hole.  Sometimes  a 
cast-iron  shoe  is  used  at  the  bottom  of  the  pipe  and  is  left  in  the  hole 
when  the  pipe  is  withdrawn. 

In  driving  through  soft  material  which  will  not  retain  its  form 
after  the  pipe  is  withdrawn,  it  is  sometimes  necessary  to  place  a  form 
of  thin  sheet  metal  inside  the  pipe  and  fill  it  with  concrete  before 
withdrawing  the  pipe.  The  soft  soil  then  fills  around  this  form  and 
does  not  mix  with  or  replace  the  concrete. 

The  Pedestal  pile  is  intended  to  give  larger  bearing  surface  at  the 
bottom  of  the  pile.  A  pipe,  or  casing,  is  driven 
into  the  ground  with  a  core  inside  which  extends 
3  or  4  feet  below  the  bottom  of  the  pipe.  The 
core  is  then  removed  and  the  hole  below  the  pipe 
is  filled  with  concrete.  The  core  is  then  rammed 
into  this  concrete,  as  shown  in  Fig.  112,  so  as  to 
force  the  concrete  into  the  earth  at  the  sidevS  of 
the  hole  and  form  an  enlarged  base  upon  which 
the  pile  may  rest,  which  procedure  is  repeated 
until  a  sufficient  volume  of  concrete  has  been 
forced  into  the  base,  the  pipe  being  then  with- 
drawn and  the  hole  filled  with  concrete. 

In  the  Gow  pile  a  casing  is  sunk  by  use  of  a 
water-jet  which  removes  the  earth  from  inside 
the  casing.  A  cutting  tool  is  then  used  to 
widen  the  hole  below  the  end  of  the  pipe,  the 
earth  being  removed  by  the  water-jet.  The  hole 
is  then  pumped  out  and  filled  with  concrete  as 
the  casing  is  removed. 

Care  is  necessary,  when  using  piles  molded  in 
place,  that  injury  to  the  pile  may  not  result  from 
disturbance  of  the  soil  around  the  pile  by 
driving  other  piles  during  the  period  of  hardening — a  danger  which 
varies  with  the  character  of  the  soil.  No  pile  should  be  driven  near 
enough  to  be  felt  in  the  earth  surrounding  a  green  pile  for  a  week  after 
it  is  placed,  unless  the  driving  can  be  done  before  the  initial  set  of  the 
concrete  takes  place. 

Pre-molded  piles  are  reinforced  like  columns  with  lateral  reinforce- 
ment of  wire  hoops,  spiral  wrappings,  or  wire  mesh,  combined  with 
longitudinal  steel  bars,  the  cross-section  most  commonly  employed 


^7 

^ 

^ 

^ 

1 

A 

i 

1 

'y 

\ 

1 

1 

1 

\ 

-  

1 

FIQ.  112. 


PILE  FOUNDATIONS  369 

being  octagonal  or  square  with  chamfered  corners.  The  diameters  in 
general  use  are  from  12  to  20  inches  for  lengths  of  20  to  50  feet, 
although  larger  and  longer  piles  are  sometimes  employed  and  they 
are  either  of  uniform  section  or  given  a  slight  taper,  according  to  the 
service  for  which  they  are  intended.  When  to  be  supported  by 
friction  upon  their  sides,  tapering  may  be  of  value  in  increasing  bear- 
ing power,  but  at  somewhat  increased  cost  of  construction.  Pointed 
shoes  are  used  at  the  bottom  to  facilitate  driving. 

Piles  are  molded  in  either  horizontal  or  vertical  position.  The 
molding  is  easier  to  handle  and  readily  subject  to  inspection  when  in 
horizontal  position.  When  molded  in  vertical  position,  the  surface  of 
concrete  as  deposited  is  normal  to  the  length  of  pile,  but  special  care 
is  necessary  in  placing  the  concrete  to  eliminate  voids.  The  rein- 
forcement is  connected  up  and  handled  as  a  unit  in  placing  in  the 
forms,  to  assure  its  proper  position  in  the  pile.  During  the  early 
period  of  hardening,  special  attention  should  be  given  to  keeping  the 
concrete  moist,  and  it  is  customary  to  allow  it  to  harden  about  thirty 
days  before  it  is  driven,  though  in  some  instances  the  hardening  has 
been  hastened  by  subjecting  the  piles  to  a  steam  bath. 

The  steel  reinforcement  in  a  pre-molded  pile  must  be  sufficient 
to  carry  the  stresses  which  occur  during  handling  and  driving  as  well 
as  those  caused  by  the  loads  which  come  upon  it  afterward.  In  rais- 
ing the  pile  from  a  horizontal  position  or  in  moving  it  horizontally, 
the  pile  must  be  capable  of  carrying  its  own  weight  as  a  beam,  sup- 
ported near  the  ends  or  at  the  middle.  Allowance  for  shocks  and 
impact  should  be  made.  After  driving,  the  pile  may  be  in  direct 
compression  when  supported  laterally  or  it  may  act  as  a  column  when 
not  so  supported.  The  concrete  used  is  ordinarily  that  known  as 
2000  pounds  concrete  of  about  1:2:4  mixture,  although  sometimes  a 
richer  mixture  is  employed. 

On  account  of  the  weight  of  concrete  piles,  heavy  drivers  are 
necessary.  Steam  hammers  are  found  most  effective  and  occasion 
less  damage  to  the  piles  than  drop  hammers.  Heavy  drop  hammers 
with  low  fall  give  better  results  than  lighter  ones  with  greater  fall. 
Caps  of  various  designs  are  employed  to  cushion  the  blow  and  pre- 
vent shattering  the  head  of  the  pile.  A  wooden  block  receives  the 
blow  of  the  hammer,  and  layers  of  old  belting,  rope  ends,  or  bags  of 
sawdust  have  sometimes  been  used  upon  the  head  of  the  pile  to  pre- 
vent the  shattering  of  the  concrete.  With  proper  precautions,  it  has 
been  found  practicable  to  drive  pre-molded  piles  without  injury  where 
heavy  driving  was  necessary. 

When  a  jet  is  to  be  used  in  driving,  a  hole  is  cast  through  the 


370 


FOUNDATIONS 


center  of  the  pile  into  which  the  jet  pipe  may  be  inserted — a  tapering 
core,  or  a  collapsible  form,  being  used  for  this  purpose,  which  is 
cheaper  than  casting  the  jet  pipe  in  the  pile.  Solid  piles  are  also  some- 
times driven  by  use  of  the  outside  jet  as  with  wooden  piles. 

There    are  several  forms  of  patented  pre-molded  piles  in  use. 


FIG.  113. 


FIG.  114. 


The  Chenowith  pile  is  formed  by  spreading  concrete  over  a  wire  mesh 
upon  a  platform,  and  rolling  it  over  a  mandrel,  the  longitudinal  rein- 
forcement being  fastened  to  the  wire  mesh.  Section  for  a  Chenowith 
pile  is  shown  in  Fig.  113.  The. Corrugated  pile  is  reinforced  with 
electrically  welded  wire  fabric,  and  is  generally  octagonal  in  cross- 


FIG.  115. 


FIG.  116.— Wakefield  Piles. 


section,  tapered,  with  grooves  cut  in  each  face.     A  section  is  shown  in 
Fig.  114. 

As  the  several  types  of  concrete  piles  have  been  devised  through 
the  need  of  meeting  differing  conditions,  each  has  advantages  for 
certain  kinds  of  service  and  is  unsuited  to  certain  other  conditions. 
Careful  determination  of  conditions  must  always  precede  choice  of 
method  of  construction. 


PILE   FOUNDATIONS 


371 


196.  Sheet  Piling. — Sheet  piles  are  made  to  fit  closely  together 
and  are  driven  in  contact  with  each  other  so  as  to  form  a  wall  to  pre- 
vent the  lateral  flow  of  soft  materials,  and  find  their  greatest  use  in 
enclosing  areas  which  are  to  be  excavated,  or  guarding  foundations 
against  undermining  by  currents  of  water.  They  are  made  of  timber, 
steel,  or  concrete. 

The  simplest  and  most  common  form  of  sheet  pile  consists  of  a 


1 


f      A 


thick  plank  sharpened  (as  shown  in  Fig.  115)  to  a  point  at  one  side  as 
so  to  cause  each  pile  to  drive  closely  against  the  one  previously 
driven.  When  heavy  timbers  are  employed,  they  are  sometimes 
arranged  with  tongue  and  groove,  which  may  be  planed  into  the 
edges  of  the  planks,  or  made  by  nailing  strips  to  the  edges.  In  some 
instances  these  are  made  to  dovetail  together. 


372  FOUNDATIONS 

Wakefield  sheet  piling  is  formed  by  bolting  and  spiking  three  planks 
together  so  as  to  form  a  tongue  on  one  edge  and  a  groove  on  the  other, 
as  shown  in  Fig.  116.  The  patent  upon  this  pile  has  expired.  They 
have  been  quite  extensively  used  in  this  country  and  for  heavy  work 
are  preferred  to  the  other  forms  of  wooden  piles.  They  are  made  of 
planks  from  1 J  to  4  inches  in  thickness,  depending  upon  the  strength 
needed  in  the  work,  and  are  bolted  together  by  pairs  of  |-inch  or 
f-inch  bolts,  6  or  8  feet  apart,  and  spiked  between  the  bolts.  The 
planks  are  12  inches  wide  and  the  tongue  is  made  as  wide  as  the  thick- 
ness of  plank,  but  not  less  than  about  2J  inches  for  the  thin  planks. 

Steel  Sheet-piling  is  made  in  a  number  of  forms  either  built  up 
from  standard  rolled  sections,  or  rolled  in  special  sections  so  that 
the  piles  may  interlock.  A  few  of  these  forms  are  shown  in  Fig.  117. 
In  form  A,  known  as  the  Jackson  pile,  two  channels  bolted  together 
with  pipe  separators  are  used  alternately  with  I-beams.  The  Frie- 
stadt  piling,  B,  consists  of  alternate  channel  bars  interlocking  with 
channels  having  Z-bars  riveted  to  them.  Form  C  is  made  up  of 
I-beams  held  together  by  a  special  locking  bar.  Forms  D  and  E 
are  special  rolled  sections,  the  ends  of  which  are  designed  to  interlock, 
and  may  be  used  in  work  curved  in  plan. 

For  temporary  work,  where  the  piling  is  to  be  removed,  steel  sheet- 
piling  is  largely  used  and  is  often  more  economical  than  timber  pil- 
ing. The  interlocking  edges  hold  the  piles  together  in  driving,  and 
give  a  certain  amount  of  transverse  strength  to  the  wall.  In  hard 
driving,  the  steel  piling  is  less  injured  than  timber  piling  and  it  may  be 
repeatedly  used. 

Reinforced  concrete  sheet-piles,  shaped  like  wooden  piles,  either 
rectangular  or  with  tongue  and  groove  on  the  edges,  are  often  used  on 
important  work  where  the  piling  is  to  be  left  permanently  in  the 
structure,  and  are  often  reinforced  with  longitudinal  bars  to  resist 
the  stresses  occurring  in  handling  and  driving.  The  loads  coming 
upon  them  after  driving  are  in  a  transverse  direction  and  the  piles 
should  be  designed  for  hydrostatic  pressure,  being  supported  laterally 
by  the  waling. 

Concrete  sheet-piling  is  sometimes  made  interlocking  by  setting 
interlocking  steel  bars  in  the  pile  edges,  the  interlocking  parts  being 
then  enclosed  in  concrete  after  driving.  In  some  instances  semi- 
circular grooves  are  left  in  the  edges  of  the  pile,  the  circular  opening 
between  the  piles  being  filled  with  concrete  after  driving. 

In  driving  sheet-piling  it  is  necessary  to  first  drive  a  row  of  guide 
piles  to  which  may  be  attached  horizontal  timbers,  or  wales,  against 
which  the  sheet  piling  may  be  driven.  The  driving  of  ordinary  sheet- 


COFFERDAMS  373 

piles  is  much  lighter  work  than  driving  bearing  piles,  and  light  steam 
hammers  are  used  for  the  purpose.  These  are  frequently  operated 
from  a  derrick  without  leads  and  may  be  handled  with  greater  rapidity 
and  less  injury  to  the  piles  than  the  ordinary  heavy  driver. 

ART.   55.     COFFERDAMS 

197.  Types  of  Cofferdams. — A  cofferdam  is  a  structure  intended 
to  exclude  water  and  soft  materials  from  an  inclosed  area,  in  order 
to  permit  the  water  to  be  pumped  out  and  the  work  of  placing  a 
foundation  to  be  done  in  the  open  air.  This  method  is  applicable 
only  to  rather  shallow  foundations,  and  for  depths  greater  than  about 
30  feet  other  methods  are  more  economical.  Cofferdams  can  be  used 
only  where  the  soil  at  the  bottom  is  fairly  impervious,  so  that  an 
excessive  flow  of  water  under  the  dam  does  not  occur. 

The  type  of  structure  for  this  purpose  varies  with  the  depth  of 
the  foundation  and  the  character  of  the  soil  upon  which  it  is  to  be 
built.  Earth,  sheet  piling,  timber  cribs,  or  combinations  of  these 
arranged  to  meet  special  conditions,  are  the  materials  employed. 

Earth  cofferdams  are  banks  of  earth  surrounding  the  area  of  the 
foundation,  and  are  made  thick  enough  to  sustain  the  pressure  of  the 
water  and  to  prevent  excessive  leakage  into  the  inclosed  space.  The 
use  of  plain  earth  dams  for  this  purpose  is  limited  to  shallow  water 
without  currents;  where  danger  of  washing  from  a  light  current 
exists,  a  wall  of  bags  filled  with  clay  and  gravel  or  a  revetment  of 
such  bags  upon  the  exposed  face  of  the  embankment  may  be  em- 
ployed. The  top  of  the  dam  should  be  at  least  2  feet  above  the  water 
surface,  and  the  top  width  not  less  than  3  feet.  A  row  of  sheet  piling 
is  sometimes  driven  and  inclosed  in  an  earth  dam  for  the  purpose  of 
reducing  the  size  of  embankment  needed,  or  of  cutting  off  a  flow  of 
water  through  the  soil  under  the  dam. 

Sheet-pile  cofferdams  are  constructed  either  of  timber  or  steel  piles 
in  single  or  double  rows,  and  are  supported  by  guide  piles,  timber 
frames,  or  cribs.  Where  a  double  row  of  sheet  piling  is  used,  a  filling 
of  earth  between  the  rows  is  necessary. 

A  crib  cofferdam  consists  of  a  timber  crib  built  so  as  to  be  water- 
tight and  is  floated  into  place  and  sunk  around  the  site  of  the  foun- 
dation. 

Movable  cofferdams  which  may  be  removed  after  using  and  sunk 
again  have  been  employed  in  a  number  of  instances.  These  may  be 
cribs  with  watertight  compartments,  or  framework  supporting  sheet 
piling. 


374 


FOUNDATIONS 


198.  Sheet-Pile  Cofferdams. — When  timber  sheet-piling  is  used 
the  most  common  form  of  cofferdam  consists  of  two  rows  of  piles 
with  a  filling  of  puddled  earth  between  them — a  system  of  construc- 
tion shown  in  Fig.  118.  Two  rows 
of  guide  piles  are  first  driven. 
Horizontal  timbers  known  as 
walls  are  attached  to  these,  and 
the  sheet-piling  driven  inside 
against  the  wales,  the  tops  of  the 
guide  piles  being  tied  together 
to  prevent  spreading  when  the 
puddle  is  put  in.  The  guide  piles 
should  be  driven  to  a  firm  bearing 
in  order  to  develop  the  transverse 
strength  of  the  pile  in  resisting 
the  water  pressure.  Horizontal 
braces  across  the  area  to  be 
drained  may  sometimes  be  used 
to  assist  the  cofferdam  against 
lateral  pressure,  and  when  this  is  not  feasible,  the  width  of  cofferdam 
must  be  made  sufficient  to  provide  lateral  strength. 

The  sheet-piling  must  be  driven  into  a  fairly  impervious  stratum 
to  prevent  leakage  under  the  dam,  and  pervious  material  overlying 
such  stratum  between  the  rows  should  be  excavated  sufficiently  to 
give  the  puddle  contact  with  the  impervious  material  below.  The 


v  *"  •  ".**.."•  *•"  '•',  '  •'.*. 

>-^_  _ 

V.Y.'"V»  ••':"?:': 

m 

N   '.'•"••   ".'*»  •    .  .' 

s;:-:  ;/  :•.'.*;.  v- 

;>'  Puddle/.' 

;:V-'-V-V  ••'/ 

m 

s                                         / 

FIG.  118. 


^          o           : 

<J          t 

O               O               0               C 

3 

C 

"V 

FIG.  119. 

puddle  needs  to  be  both  impervious  and  stable,  and  a  mixture  of  gravel 
and  clay  is  desirable  for  the  purpose.  Clay  is  impervious  but  washes 
easily  if  the  water  finds  an  opening  through  it,  while  gravel  or  coarse 
sand  mixed  with  the  clay  tends  to  prevent  such  washing.  The  thick- 
ness of  puddle  required  depends  upon  its  quality  and  upon  the  pres- 
sure to  be  resisted,  a  thickness  of  one-fourth  to  one-sixth  of  the  depth 
being  usually  sufficient.  For  best  results,  the  puddle  should  be 
placed  in  thin  layers  and  well  tamped  in  damp  condition. 


COFFERDAMS  375 

A  single  wall  of  sheet-piling  is  often  used  supported  by  guide 
piles  or  by  an  interior  framework — a  method  which  requires  less 
space  than  the  puddle  wall  type  and  is  preferable  where  it  is  important 
not  to  restrict  the  water  way.  Plan  of  a  cofferdam  of  this  type  for 
use  in  constructing  a  bridge  pier  is  shown  in  Fig.  119.  The  guide 
piles  are  first  driven,  wales  attached,  and  the  sheet-piles  driven 
against  the  outside  waling.  Braces  from  wall  to  wall  across  the 
opening  are  used  to  assist  in  resisting  the  lateral  pressure.  Such 
bracing  when  needed  may  be  placed  at  lower  levels  as  the  water  is 
pumped  out  and  excavation  proceeds. 

When  guide  piles  cannot  be  driven  to  firm  bearing,  timber  frames 
are  sometimes  used  to  act  as  guides  and  support  the  sheet-piling 
against  lateral  pressure.  These  frames  may  be  built  upon  the  ground, 
floated  to  the  site  and  sunk  into  position.  The  sheet-piles  are  then 
driven  around  the  frames  so  as  to  inclose  it. 

Interlocking  steel  piling  is  often  employed  for  single  wall  work 
because  of  its  greater  strength  and  tightness.  Timber  piling  for 
such  use  should  be  tongued  and  grooved.  Wakefield  piling  has  most 
frequently  been  used. 

Some  leakage  is  always  to  be  expected  in  cofferdams,  and  in 
many  instances  special  precautions  are  necessary  to  exclude  water. 
The  possibility  of  meeting  difficulty  in  preventing  leakage  is  the  prin- 
cipal objection  to  this  method  of  construction.  Banking  clay  against 
the  outside  of  the  cofferdam  is  a  common  expedient  to  prevent  leak- 
age through  or  immediately  under  the  dam.  When  it  is  feared  that 
channels  may  open  under  the  piling,  gravel  may  be  deposited  around 
the  base  of  the  dam  to  close  such  incipient  openings.  Tarpaulins  are 
often  employed  to  cover  the  outside  of  the  dam,  or  spread  out  upon  the 
bottom  outside  the  base  of  the  dam  and  weighted  with  gravel.  When 
the  bottom  is  rock,  it  is  sometimes  necessary  to  cover  the  whole  area 
inside  the  cofferdam  with  a  layer  of  concrete  to  prevent  inflow  of 
water  through  seams  in  the  rock. 

199.  Crib  Cofferdams. — Timber  cribs  built  on  land  and  floated 
into  position  are  frequently  used  as  cofferdams,  and  for  shallow 
depths,  these  may  be  made  of  a  framework  of  timber  with  a  covering 
of  planks  upon  the  outside.  Usually  the  crib  is  formed  of  two  walls 
made  of  squared  timbers  laid  on  top  of  each  other,  tied  together,  and 
braced  with  framework,  and  is  sunk  by  loading  with  gravel  or  earth, 
and  sometimes  filled  with  puddle  to  increase  its  watertightness. 
The  crib  itself  may  be  made  practically  water-tight,  so  that  leakage  is 
restricted  to  the  space  below  the  crib.  In  using  this  method  there  are 
no  braces  across  the  space  in  which  the  foundation  is  to  be  placed. 


376  FOUNDATIONS 

The  bottom  should  be  leveled  before  sinking  the  crib,  or  when  on 
bed  rock,  the  bottom  of  the  crib  may  be  made  approximately  to  fit 
the  surface  of  the  rock.  Sheet  piling  may  be  driven  around  the 
outside  of  the  crib  to  prevent  leakage  under  the  crib  when  the  crib 
does  not  lie  upon  the  rock.  Tarpaulins  fastened  to  the  crib  near 
the  bottom  are  frequently  used  to  prevent  leakage  under  the  crib. 
A  deposit  of  puddle  around  the  base  of  the  crib  is  generally  sufficient 
to  seal  the  bottom  against  excessive  leakage  in  ordinary  work,  but 
a  layer  of  concrete  over  the  rock  bottom  is  sometimes  necessary. 

Cribs  are  sometimes  made  so  that  they  may  be  removed  and  re- 
peatedly used.  These  have  sometimes  been  used  for  bridge  piers, 
being  made  in  two  parts  joining  together  on  the  short  sides  so  that  they 
may  be  taken  from  around  the  foundation  after  it  is  constructed. 
Watertight  compartments  are  provided  which  may  be  pumped  out 
when  it  is  desired  to  float  the  cribs.  Sometimes  sheet-piling  is  used 
around  these  cribs,  which  may  be  withdrawn  before  raising  them. 

ART.   66.    BOX  AND   OPEN   CAISSONS 

200.  Box  Caissons. — A  caisson  is  a  watertight  casing  within  which 
the  work  of  placing  a  foundation  may  be  done.  The  casing  forms 
a  shell  which  contains  and  usually  remains  a  permanent  part  of  the 
foundation.  Caissons  are  of  three  general  types:  Those  closed  at 
bottom,  known  as  box  or  erect  caissons;  those  open  at  both  top  and 
bottom,  known  as  open  caissons;  and  those  closed  at  top,  called  pneu- 
matic or  inverted  caissons. 

Box  caissons  of  timber  are  commonly  employed  when  masonry 
foundations  are  to  be  placed  upon  piles  cut  off  under  water.  These 
caissons  are  water-tight  boxes,  open  at  the  top,  which  may  be 
floated  into  position  over  the  piles  upon  which  they  are  to  rest  and 
then  sunk  by  building  the  masonry  inside  them.  The  floor  and  lower 
part  of  the  caisson  is  usually  a  permanent  part  of  the  foundation,  but 
the  sides  which  extend  above  the  water  are  intended  to  act  as  coffer- 
dams during  construction  of  the  masonry  and  are  removed  upon  com- 
pletion of  the  work. 

The  construction  of  box  caissons  varies  with  the  depth  of  water 
in  which  they  are  to  be  sunk  and  the  shape  and  dimensions  of  the 
foundations.  For  light  work,  timber  studding  with  plank  sides  and 
bottom  may  be  sufficient,  while  in  heavier  work,  a  bottom  of  two  or 
more  thicknesses  of  12X12  inch  timbers,  with  sides  built  up  of 
similar  timbers  on  top  of  each  other,  and  drift-bolted  together,  or 
timber  framework  with  vertical  staves  may  be  used.  The  bottom 


BOX  AND  OPEN  CAISSONS  377. 

must  be  capable  of  carrying  the  load  of  masonry  required  for  sinking 
and  the  sides  must  resist  the  water  pressure  or  the  outward  pressure  of 
material  with  which  it  may  be  filled.  The  caisson  may  be  built  on 
land,  launched  and  floated  to  the  site  of  the  foundation,  or  when 
heavy  timbers  are  to  be  used  for  a  floor,  it  may  more  easily  be  built 
afloat. 

Timber  box  cissons  are  occasionally  used  as  a  base  for  foundations 
upon  fairly  firm  soil.  The  excavation  must  be  made  to  the  depth 
required  before  the  caisson  is  sunk.  Such  caissons  were  used  in  the 
foundations  of  the  south  pier  of  the  Duluth  Ship  canal.  "They 1 
were  from  24  to  36  feet  wide,  21  feet  high,  and  from  50  to  100  feet 
long.  The  floor  was  8  inches  thick  laid  close,  the  channel  side  had 
a  solid  wall  of  a  double  thickness  of  12  X 12  inch  timbers,  while  the 
opposite  side  was  composed  of  a  single  thickness  of  12X12  inch 
timbers  laid  close.  Connecting  and  bracing  the  two  walls  were  trans- 
verse bulkheads  of  10X12  inch  material  spaced  4  feet  center  to 
center  horizontally. 

"The  caissons  were  built  in  the  harbor,  towed  to  the  site,  and  sunk 
by  filling  with  rock  and  gravel.  After  sinking,  the  caissons  were  cov- 
ered with  a  layer  of  heavy  timbers,  in  which  was  built  the  concrete 
pier,  the  top  of  the  caisson  being  slightly  below  low  water  level." 

For  work  of  this  kind,  a  timber  crib  or  grillage  which  is  not  water- 
tight is  sometimes  used  for  the  lower  part  of  the  foundation,  the  top 
of  the  crib  being  below  low  water.  A  box  caisson  is  then  sunk  on  top 
of  the  crib.  The  floor  of  the  caisson  carries  the  masonry  superstruc- 
ture, and  the  sides,  which  are  intended  only  to  exclude  water  during 
construction,  are  removed  when  no  longer  needed.  Reinforced- 
concrete  box  caissons  have  been  used  in  some  instances.  They  may 
be  made  part  of  the  permanent  structure  above  as  well  as  below  the 
low  water  level,  and  do  not  need  the  cofferdam  sides. 

Box  caissons  of  small  size  have  sometimes  been  sunk  several  feet 
into  soft  material  by  the  use  of  water  jets  under  the  bottom.  A 
number  of  pipes  are  run  through  the  bottom  to  carry  the  water, 
which  washes  the  material  from  underneath  and  allows  the  caisson 
to  sink. 

201.  Types  of  Open  Caissons. — An  open  caisson  consists  of  a 
casing,  with  one  or  more  openings  extending  through  from  top  to 
bottom,  intended  to  be  sunk  through  soft  materials  which  may  be 
displaced  by  the  weight  of  the  caisson  or  removed  by  dredging 
through  the  openings.  The  caisson  is  always  an  integral  part  of 
the  foundation.  It  may  be  simply  a  shell  to  contain  concrete  upon 
1  Jacoby  and  Davis,  Foundations  of  Bridges  and  Buildings,  p.  243. 


378  FOUNDATIONS 

which  the  main  reliance  for  strength  is  placed,  or  the  caisson  itself 
may  be  designed  to  bear  the  loads  coming  upon  the  foundation  and 
the  filling  for  the  purpose  of  sinking  and  anchoring  it. 

The  open-caisson  method  is  extensively  used  and  has  been  em- 
ployed in  placing  foundations  when  the  depth  is  too  great  for  any 
of  the  other  methods  in  common  use.  The  caissons  may  be  made  of 
timber,  steel,  or  concrete,  and  vary  widely  in  design,  according  to  the 
size  and  character  of  the  foundation  to  be  constructed.  Three  types 
of  open  caissons  are  in  use:  (1)  Single-wall  caissons  of  timber, 
consisting  of  an  outer  watertight  wall  with  the  bracing  necessary 
to  enable  it  to  hold  its  form;  (2)  cylinder  caissons,  consisting  of  a 
single  or  double  cylindrical  shell  of  steel  or  concrete  with  a  single 
opening  at  the  center;  (3)  caissons  having  several  openings  or  wells, 
with  double  walls  between  and  around  them.  The  double  walls  are 
joined  at  bottom  into  cutting  edges,  and  the  spaces  between  them 
filled  with  concrete  or  other  materials  to  aid  in  sinking. 

Caissons  of  the  first  type  are  used  where  the  depth  of  sinking  is 
small  or  the  material  through  which  they  are  to  be  sunk  is  soft. 
They  are  frequently  employed  for  piers  where  the  foundation  is  upon 
rock  with  little  or  no  soil  above  it,  and  a  shell  is  needed  within  which 
the  concrete  body  of  the  pier  may  be  formed.  Cylinder  caissons  are 
used  for  foundations  of  small  area  which  must  be  sunk  to  consider- 
able depths  through  soft  materials.  The  method  with  several  open- 
ings is  used  for  larger  foundations  requiring  sinking  to  considerable 
depths. 

203.  Single-wall  Timber  Caissons. — Single-wall  caissons  are 
constructed  in  the  same  manner  as  box  caissons,  without  the  bot- 
toms. The  walls  are  commonly  built  up  with  12X12  inch  timbers 
or  with  12  inch  plank  laid  flat.  They  are  sunk  upon  a  bottom  of 
rock  or  other  firm  material  which  has  been  prepared  to  receive 
them.  It  is  then  only  necessary  to  provide  an  outer  wall  of  the 
form  desired  for  the  foundation,  with  bracing  to  resist  the  water 
pressure  when  pumped  out,  and  a  means  of  carrying  sufficient  load 
to  sink  it. 

When  the  site  is  covered  with  soft  material,  sinking  is  accomplished 
by  weighting  the  top  of  the  caisson  with  some  material  which  may 
afterward  be  removed,  by  dredging  the  soil  from  inside  the  bottom, 
and  sometimes  by  using  a  water-jet  to  wash  the  soil  from  under  the 
walls.  After  sinking,  the  bottom  is  sealed  with  concrete  deposited 
under  water  and  the  caisson  pumped  out,  after  which  the  concrete 
filling  may  be  placed  in  the  open  air.  In  some  instances  the  filling  is 
all  placed  through  the  water  without  pumping  out  the  caisson,  in 


BOX  AND  OPEN  CAISSONS 


379 


which  case,  it  would  not  be  necessary  that  the  caisson  be  water-tight, 
but  it  must  be  capable  of  holding  the  concrete  filling. 

The  permanent  portion  of  a  timber  caisson  usually  terminates 
below  low  water,  the  part  extending  above  the  water  being  removed 
after  serving  as  a  cofferdam  within  which  the  masonry  has  been  con- 
structed. 

In  constructing  the  Columbia  River  Bridge  of  the  North  Coast 
Railway,1  open  caissons  were  used  to  provide  forms  for  the  con- 
struction of  concrete  piers  upon  the  hard  bottom  of  the  river.  The 
depth  of  water  was  about  30  feet  and  velocity  of  current  seven  miles 
per  hour.  The  construction  of  the  caissons  is  shown  in  Fig.  120. 


FIG.  120. 


The  walls    consisted    of 

12X12     inch    timbers 

framed    and    braced    to 

conform  to  the  shape  of 

the    pier.      The    caisson 

was    sunk  by  weighting 

with  rails  held  in  racks 

upon  the  sides  in  order 

to  keep  the  load  near  the 

bottom  and  prevent  capsizing.     The  concrete  was  deposited  through 

the  water  to  the  depth  of  32  feet,  large  buckets  with  movable  bottoms 

being  used  for  the  purpose. 

In  the  construction  of  a  pivot  pier  on  rock  foundation,  the  En- 
gineering Department  of  Boston  used  a  single-wall  circular  caisson  60 
feet  in  diameter  and  30  feet  high  as  a  form  for  the  concrete  body  of 
the  pier.  The  caisson  was  built  of  about  145  courses  of  3X12  inch 
yellow  pine  planks,  8  feet  long,  laid  flat  and  breaking  joints.  The 
ends  were  beveled  to  make  radial  joints,  and  each  plank  secured  to 

1  Engineering  News,  Oct.  5,  1911,  p.  392. 


380  FOUNDATIONS 

those  below  it  by  1-inch  oak  tree  nails  9  inches  long,  two  at  each  end 
of  each  plank.  In  addition,  the  planks  were  well  spiked  to  the  lower 
courses  throughout  their  lengths  with  6-inch  spikes.  The  courses 
were  also  secured  together  by  4X12  inch  vertical  planks  opposite 
alternate  joints. 

Before  placing  the  caisson,  the  site  was  dredged  to  rock.  "  There 1 
was  no  attempt  to  construct  the  crib  so  that  on  the  bottom  it  should 
conform  to  the  variations  in  the  rock  surface.  Instead,  the  bottom 
of  the  crib  was  made  level  and  it  was  sunk  until  it  took  bearing 
on  only  a  portion  of  the  lower  edge  at  the  highest  rock  level.  Then 
to  provide  continuous  bearing  to  all  parts  of  the  circumference,  and 
especially  to  complete  the  inclosure  of  the  crib  and  confine  the  con- 
crete that  was  afterward  deposited  within  it,  wooden  boxes  of  vary- 
ing sizes,  but  averaging  about  4  feet  square  and  4  feet  deep,  were  filled 
with  lean  concrete,  lowered  to  the  bottom  and  placed  by  divers  under 
the  edge  of  the  crib  to  form  a  continuous  wall.  After  the  concrete 
boxes  were  placed,  the  excavation  outside  the  crib  was  back-filled 
with  gravel  until  the  whole  crib  was  surrounded  by  filling  to  about  29 
feet  below  low  water  or  some  2  feet  above  the  bottom  courses  of  plank. 
This  backfilling  formed  an  effectual  seal  to  retain  the  concrete  which 
was  deposited  in  water  inside  the  crib  without  un watering  the  crib." 

203.  Cylinder  Caissons. — The  method  of  sinking  wells  by  using  a 
curbing  of  brick  masonry  which  sinks  as  the  earth  is  excavated  from 
the  bottom  has  been  in  common  use  for  many  years.  A  wooden  cut- 
ting edge  is  constructed  and  the  brickwork  started  on  top  of  this  and 
built  up  as  the  sinking  progresses.  This  method  has  been  used  for  a 
long  time  in  India  for  bridge  foundations  and  in  a  number  of  instances 
in  Europe.  Usually  work  of  this  character  has  been  of  small  diam- 
eter and  sunk  to  comparatively  shallow  depths,  but  in  some  in- 
instances  large  shafts  have  been  sunk  by  this  method,  and  depths  of 
over  200  feet  have  been  reached. 

Circular  caissons  of  metal  and  reinforced  concrete  have  come  into 
use  more  recently  and  are  frequently  employed  where  foundations  of 
small  area  are  feasible,  and  in  a  few  instances  for  foundations  of 
larger  area  where  circular  piers  are  to  be  constructed.  They  are 
frequently  used  for  the  foundations  of  highway  bridges  where  con- 
siderable depths  must  be  reached,  a  pair  of  cylinders  braced  together 
being  employed  for  each  pier.  Circular  caissons  of  small  diameter 
are  constructed  with  single  walls  and  a  cutting  edge  at  the  bottom, 
those  of  larger  diameters  having  double  walls  with  space  between  the 
walls  for  loading  with  concrete. 

1  Engineering  Record,  Aug.  2,  1913. 


BOX  AND  OPEN  CAISSONS  381 

Steel  walls  are  commonly  used  for  circular  caissons  in  this  country, 
although  small  sections  are  frequently  of  cast-iron  pipe  resting  upon  a 
steel  cutting  edge.  In  the  foundations  of  the  California  City  Point 
Coal  Pier,  4-foot  cast-iron  pipe  was  used  in  lengths  of  12  feet  bolted 
together.1  A  conical  steel  section  8  feet  in  diameter  was  used  at  the 
bottom  to  give  large  bearing  area,  and  the  concrete  filling  in  the  pipe 
was  reinforced  with  vertical  steel. 

In  constructing  foundations  for  torpedo  boat  berths  at  Charleston, 
S.  C.,  steel  cylinders  8  feet  in  diameter  and  42  to  52  feet  long  were 
used  as  cofferdams.2  The  cylinders  were  sunk  through  a  bed  of  sand 
and  about  4  feet  into  a  bed  of  blue  clay,  which  sealed  the  bottom,  the 
soil  inside  being  then  excavated  to  near  the  bottom.  Some  wooden 
piles  45  feet  long  were  driven  inside  the  cylinder  and  the  bottom 
section  5  feet  deep  filled  with  concrete,  inclosing  the  tops  of  the  piles. 
A  form  was  then  set  up  inside  the  cylinder  and  4-foot  reinforced  con- 
crete columns  constructed  to  the  top,  the  forms  and  cylinder  above 
the  bottom  section  being  then  removed. 

Cylinders  8  feet  in  diameter  were  used  for  the  foundations  of  the 
bridge  over  the  Atchafalaya  at  Morgan  City,  La.  (see  Baker's 
Masonry  Construction) .  These  were  sunk  to  a  depth  of  120  feet  below 
high  water  and  from  70  to  115  feet  below  the  mud  line.  Below  the 
river  bottom,  the  cylinders  were  of  cast  iron  1 J  inches  thick  and  above 
of  wrought  iron  f  inch  thick. 

A  double-wall  caisson  of  steel  was  used  for  the  pivot  pier  of  the 
Omaha  Bridge  and  Terminal  Company's  bridge  across  the  Missouri 
River  at  Council  Bluffs,  Iowa.3  The  caisson  was  of  steel,  40  feet 
outside  and  20  feet  inside  diameter  and  was  sunk  through  sand  and 
clay  and  coarse  sand  to  the  rock  120  feet  below  low  water.  The 
spaces  between  the  walls  were  filled  with  concrete  to  furnish  weight 
for  sinking.  In  sinking,  the  material  was  dredged  from  inside  the 
caisson,  and  water  jets  were  used  upon  the  outside  to  reduce  the 
friction.  Twenty  3-inch  vertical  pipes  were  carried  down  inside  the 
outer  cylinder  to  the  cutting  edge  to  provide  for  operation  of  water 
jets. 

Reinforced  concrete  walls  are  gradually  coming  into  use  for  cylinder 
caissons  and  seem  to  offer  advantages  for  the  purpose.  The  weight 
of  concrete  is  of  help  in  sinking  and  obviates  the  necessity  of  so  much 
temporary  loading,  which  is  an  item  of  considerable  expense,  while 
the  greater  durability  of  the  concrete  as  compared  with  steel  is  also 


1  Engineering  News,  June  27,  1908. 

2  Engineering  News,  Nov.  11,  1915. 

3  Engineering  Record,  Jan.  24,  1903, 


382  FOUNDATIONS 

of  value.  Gravel  filling  may  sometimes  be  employed  in  a  reinforced 
concrete  cylinder,  while  the  steel  cylinder  should  be  filled  with  con- 
crete. 

Concrete  cylinders  are  cast  in  place  by  using  adjustable  forms  for 
building  up  the  upper  end  as  the  cylinder  is  sunk.  •  In  some  instances, 
however,  they  are  cast  in  sections  off  the  work  and  placed  in  position 
after  hardening. 

Reinforced  concrete  cylinder  caissons  were  used  in  the  foundations 
of  the  lumber  docks  at  Balboa,  Canal  Zone.1     The  caissons  were 
made  8  feet  in  outside  and  6  feet  in  inside  diameter  and  were  pre-cast 
in  sections  6  feet  long.     The  bottom  sections  had  conical  exterior  sur- 
faces, widening  to  10  feet  in  diameter 
and  fitted  into  a  cutting  edge  made  of 
steel  plates  as  shown  in  Fig.  121.     The 
sections  were  reinforced  with   vertical 
bars  and  horizontal  rings  of  steel,  and 
were  fastened  together  by  means  of  six 
1-inch  anchor  bars  12  feet  long,  which 
pass  through  cores  molded  in  the  shell. 
The  rods  were  fastened  together  by  the 

use  of  sleeve  nuts  which  were  adjusted  in  niches  molded  in  the 
shell  for  the  purpose. 

The  caissons  were  sunk  60  to  70  feet  to  rock,  by  laborers  excavating 
inside  of  them,  the  water  being  kept  down  by  pumping.  The  cutting 
edge  was  embedded  about  a  foot  in  the  rock,  and  a  conical  depression 
was  blasted  out  of  the  rock  in  the  center  to  give  the  concrete  filling  a 
strong  bond. 

Caissons  having  shells  6J  feet  in  outside  and  4J  feet  in  inside 
diameter  were  used  in  the  foundations  for  the  Penhorn  Creek  Viaduct 
of  the  Erie  Railroad.2  They  were  reinforced  with  ^-inch  horizontal 
rings  spaced  6  inches  apart.  The  caissons  were  built  in  place  in 
sheeted  pits,  12  feet  square  and  15  feet  deep,  collapsible  steel  forms 
5  feet  long  being  used  and  29  feet  of  caisson  built  at  one  operation, 
which  after  being  allowed  to  set  was  sunk  and  another  section  added, 
depths  of  about  70  feet  being  reached  in  this  way.  The  concrete  was 
allowed  to  harden  six  days  before  sinking,  which  was  accomplished 
by  dredging  with  an  orange  peel  bucket,  and  sometimes  using  a 
water  jet.  The  jets  were  usually  necessary  below  depths  of  about 
40  feet.  Four  1  J-inch  pipes  suspended  from  the  derricks  and  guided 
by  hand  were  employed.  .  The  jets  were  used  around  the  upper  part 

1  Engineering  Record,  July  20,  1912. 

2  Engineering  News,  Oct.  13,  1910. 


BOX  AND  OPEN  CAISSONS  383 

of  the  exterior  faces  of  the  caissons  to  within  about  20  feet  of  the 
bottom. 

Concrete  cylinder  caissons  6  feet  in  outside  diameter,  8  inches 
thick  and  from  33  to  55  feet  deep  were  used  in  the  foundations  for  the 
storehouse  of  the  Boston  Army  Supply  Base;  577  of  these  piers  were 
placed  in  110  working  days.1  Pits  12  feet  deep  and  10  feet  4  inches 
square  were  dug  and  concrete  cylinders  22  feet  high  constructed  in  the 
pits.  The  caissons  were  sunk  below  the  bottoms  of  the  pits  by  men 
digging  the  earth  from  inside  them  and  forcing  them  down  by  the  use 
of  jacks.  The  forms  were  removed  and  excavation  begun  twenty-four 
hours  after  pouring  the  concrete.  When  a  sufficient  depth  could  not 
be  reached  by  this  method,  the  concrete  cylinder  was  continued  at  the 
bottom  in  open  cut  behind  poling  boards.  After  the  concrete  shell 
reached  solid  clay,  the  hole  was  belled  out  below  the  end  of  the  shell 
to  give  a  larger  bearing  to  the  base  of  the  pier  and  the  whole  filled 
with  concrete.  Ground  water  was  kept  down  by  constant  pumping. 

204.  Dredging  through  Wells. — When  foundations  are  to  be 
sunk  to  considerable  depths  through  soft  materials,  the  method  of 
dredging  through  wells  is  very  commonly  employed,  wherein, 
caissons  of  wood,  steel,  or  concrete  are  built  with  vertical  openings,  or 
wells,  extending  through  them.  The  body  of  the  caisson  surround- 
ing the  wells  is  filled  with  concrete  to  provide  weight  for  sinking,  and 
the  soil  at  the  bottom  is  removed  by  dredging  through  the  wells,  or 
by  men  in  open  excavation  when  the  water  can  be  kept  down  by 
pumping. 

When  the  foundation  is  to  be  sunk  through  deep  water,  the  cais- 
sons may  be  built  on  land  or  on  barges  and  floated  to  the  site.  When 
the  site  for  the  foundation  is  on  land  or  in  shallow  water,  the  caisson 
may  be  started  in  place,  in  an  open  cut  or  inside  of  cofferdams,  and 
built  up  as  the  sinking  proceeds.  As  the  position  of  the  caisson  can- 
not be  accurately  controlled  in  sinking,  it  is  necessary  to  make  the 
horizontal  area  covered  by  it  larger  than  that  of  the  foundation  it  is 
to  carry.  In  a  large  caisson,  the  descent  is  guided  by  the  manner  of 
excavation,  when  resistance  is  met  upon  one  end  which  tends  to  tip 
the  caisson,  the  excavation  is  confined  to  that  end  until  it  is  righted. 
If  the  caisson  is  narrow  and  the  wells  in  one  line,  the  control  in  a 
transverse  direction  is  often  difficult.  Obstructions,  such  as  boulders 
or  sunken  logs  under  the  cutting  edges,  offer  the  most  serious  obstacles 
to  work  of  this  kind.  These  are  not  met  at  great  depths  and  are  com- 
monly removed  by  divers,  or  sometimes  by  the  use  of  a  water 
jet. 

1  Engineering  News-Record,  Sept.  24,  1918. 


384  FOUNDATIONS 

Timber  caissons  have  been  employed  more  frequently  than  metal 
ones  in  this  country. 

The  first  use  of  deep  open  caissons  in  America  was  in  the  con- 
struction of  the  foundations  of  the  Poughkeepsie  bridge  over  the 
Hudson  River.1  The  largest  of  these  caissons  was  60  X 100  feet  in 
plan  for  the  bottom  40  feet,  narrowing  to  40  feet  in  width  at  the  top. 
There  were  14  wells,  each  10  X 12  feet,  separated  by  one  longitudinal 
and  six  transverse  walls.  The  cutting  edges  at  the  bottom  were 
12X12  inch  white-oak  timbers,  and  the  walls  were  of  hemlock,  solid 
and  triangular  in  shape  for  the  lower  20  feet,  widening  at  that  height 
to  their  full  widths.  The  end  walls  and  longitudinal  walls  were 
hollow  above  this  height.  The  six  transverse  walls  were  solid  and  2 
feet  thick  for  the  full  height. 

The  hollow  walls  were  filled  with  gravel  in  sinking  the  crib  and 
the  soil  was  excavated  through  the  wells  with  a  clam-shell  bucket. 
The  caisson  was  104  feet  high  and  was  sunk  until  the  top  was  23  feet 
below  low  water,  the  last  dredging  being  done  with  the  top  submerged. 
The  wells  were  then  filled  with  concrete,  and  a  box  caisson  with  bottom 
of  grillage  6  feet  thick  was  sunk  on  top  and  the  masonry  of  the  pier 
built  up  in  this  as  a  cofferdam,  the  sides  being  removed  when  the 
masonry  was  above  water. 

Open  timber  caissons  were  used  in  the  foundations  of  the  bridge  of 
the  Oregon  Railway  and  Navigation  Company  across  the  Willamette 
River  at  Portland,  Oregon.2  They  were  36X72  feet  with  six  well 
holes,  each  9  feet  square,  the  cutting  edges  being  made  of  steel  plates 
inclosing  the  bottom  timbers,  with  6  X  6  X  f-inch  angles  at  the  bottom. 
The  lower  1 1  feet  of  the  crib  was  of  solid  timber,  triangular  in  shape, 
with  vertices  at  the  cutting  edges.  Above  that  height,  walls  12  inches 
thick  were  carried  up  and  the  entire  spaces  around  the  wells  filled 
with  concrete  as  the  caissons  were  sunk.  The  caissons  rest  upon 
cemented  gravel  120  and  130  feet  below  low  water,  and  when  in  final 
position  the  wells  were  filled  with  concrete.  The  crib  proper  ends  at 
20  feet  below  low  water  and  the  upper  part  of  the  caissons  were  built 
to  be  used  as  cofferdams  within  which  the  superstructure  of  the  pier 
could  be  constructed. 

"In  the  construction  of  each  of  these  piers  a  substantial  dock  was 
first  constructed  in  the  river,  consisting  of  about  100  piles  well  driven 
down,  capped,  and  braced  together.  Borings  were  then  made  around 
the  entire  perimeter  of  the  crib  at  spaces  about  8  feet  apart,  and  the 
elevations  of  hard  material  at  all  points  were  determined.  It  was 

1  Transactions,  American  Society  of  Civil  Engineers,  June,  1888. 

2  Railway  Age-Gazette,  July  14,  1911. 


BOX  AND  OPEN  CAISSONS  385 

found  to  be  on  a  considerable  slope,  showing  a  difference  of  elevation 
of  22  feet  for  opposite  diagonal  corners.  When  these  elevations  were 
determined,  pipes  were  successively  sunk  at  numerous  points  around 
the  perimeter  and  in  the  location  of  the  cross  walls,  and  holes  drilled 
in  the  hard  material  to  a  common  level  some  2  feet  below  the  lowest 
elevation  of  the  top  of  the  cemented  gravel.  As  soon  as  the  drilling 
at  each  hole  had  been  completed  to  the  proper  elevation,  a  cartridge  of 
black  powder  and  dynamite  in  a  sheet  iron  case  was  lowered  to  the 
bottom  of  the  hole  and  discharged  by  an  electric  battery.  This 
process  was  repeated  at  such  frequent  intervals  as  it  was  deemed  would 
produce  a  bottom  uniform  in  character  throughout  the  entire  area  of 
the  crib.  Thus  the  blasting  for  leveling  the  cemented  gravel  was 
carried  on  before  an  excavation  was  made  through  50  feet  of  gravel 
and  sand.  In  the  meantime  the  steel  cutting  edge  had  been  set  up 
and  riveted  together  on  ways  in  a  shipyard  convenient,  and  enough 
timber  put  on  to  float  the  crib,  which  in  this  condition  was  some  30 
feet  high.  It  was  then  floated  into  position  in  the  dock  already  pre- 
pared and  other  piles  driven  on  the  open  end  of  the  dock,  entirely 
inclosing  the  crib." 

Iron  and  steel  caissons  have  been  extensively  used  by  English 
engineers,  but  in  this  country  the  use  of  metal  has  usually  been 
restricted  to  the  cylindrical  form,  as  timber  has  generally  been 
found  cheaper  and  more  satisfactory. 

The  foundations  of  the  Hawkesbury  bridge  in  Australia  is  a 
notable  example  of  this  method.  The  caissons  were  of  wrought 
iron,  48  feet  long  and  20  feet  wide,  with  semicircular  ends.  Three 
circular  dredging  wells  were  used,  8  feet  in  diameter  and  14  feet 
between  centers.  The  pockets  around  and  between  the  wells  were 
filled  with  concrete  to  aid  in  sinking  the  caisson,  and  the  sides  and 
filling  were  continually  built  up  as  the  sinking  progressed.  The 
caissons  were  bedded  upon  sand,  the  maximum  depth  reached  being 
162  feet  below  high  water,  through  108  feet  of  mud  and  silt. 

The  bottoms  of  the  caissons  were  made  flaring  for  the  lower  20 
feet,  making  the  bottom  2  feet  wider  all  around,  this  arrangement 
being  intended  to  reduce  friction  on  the  sides,  but  it  was  found  to 
increase  seriously  the  difficulty  of  guiding  the  caisson.  When  the 
soil  is  not  uniform  over  the  base,  there  is  a  tendency  to  travel  toward 
the  firmer  material,  which  was  obviated  by  making  the  surfaces  of  the 
wider  bottom  sections  vertical  instead  of  flaring,  with  an  offset  about 
20  feet  above  the  cutting  edge. 

Concrete  open  caissons  are  rapidly  coming  into  use  and  possess 
many  advantages  where  they  may  be  built  in  place  and  started  in  the 


386 


FOUNDATIONS 


open  air.  When  the  wells  are  filled  with  concrete,  it  makes  a  mono- 
lithic structure,  with  no  parts  subject  to  decay  or  corrosion,  and 
when  heavy  walls  are  used,  the  weight  is  of  advantage  in  sinking. 
Reinforcement  is  usually  employed,  although  in  a  few  instances  heavy 
shells  have  been  sunk  without  reinforcement.  Light  reinforcement 
seems  desirable  in  nearly  all  cases  as  having  additional  security 
against  cracking. 

The  method  of  dredging  through  wells  was  used  in  sinking  con- 
crete caissons  for  the  foundations  of  the  Pittsburgh  &  Lake  Erie 
Railroad  bridge  at  Beaver,  Pa.  The  caissons  were  80  feet  long  and  28 
feet  wide  with  semicircular  ends.  The  shell  was  7  feet  thick  with  two 


\/ 


;4-; 
W 


13 


FIG.  122. — Concrete  Caisson. 

cross-walls  each  5  feet  thick,  and  was  tapered  in  the  lower  9  feet  to 
the  cutting  edge  of  steel.  Rectangular  cofferdams  were  constructed 
around  the  site  in  about  7  feet  of  water  and  pumped  out.  The  cais- 
sons were  then  built  inside  the  cofferdams  and  sunk  through  about  38 
feet  of  sand  and  gravel  to  the  rock.  When  they  had  been  sunk  nearly 
to  the  rock  by  dredging  through  the  open  walls,  they  were  transformed 
into  pneumatic  caissons  and  bedded  upon  the  rock  by  the  pneumatic 
process. 

Fig.  122  shows  a  reinforced-concrete  caisson  used  in  the  foundation 
of  a  pier  of  the  American  River  bridge  of  the  Southern  Pacific  Rail- 
road.1 It  was  76  feet  long,  28  feet  wide,  and  22  feet  high,  with  a  shell 
3  feet  thick  and  three  cross-walls  each  4  feet  thick,  and  was  built  when 
the  stream  was  dry  in  a  pit  dug  to  the  level  of  ground  water,  being 
1  Engineering  Record,  August  27,  1910. 


PNEUMATIC  CAISSONS  387 

sunk  by  dredging  through  the  four  wells.  When  the  top  of  the  caisson 
reached  the  ground  level,  a  timber  cofferdam  was  constructed  on  top. 
The  sinking  was  then  continued  until  the  stratum  of  cobbles  and 
boulders  upon  which  it  was  to  rest  was  reached.  The  wells  were  then 
filled  with  concrete  and  the  pier  built  up  in  the  cofferdam.  This 
caisson  was  very  light  in  weight  and  the  sinking  so  slow  that  it  was 
found  more  economical  to  construct  the  other  piers  by  excavating 
inside  of  sheet  iron  cofferdams. 

In  constructing  the  channel  pier  of  the  North  Side  Point  bridge 
over  Allegheny  River  at  Pittsburgh,  a  concrete  caisson  83JX23  feet 
was.  used,  with  4  wells  10X9  feet  spaced  19  feet  between  centers.1 
When  the  caisson  reached  a  height  of  31  feet,  with  the  cutting  edge 
17  feet  below  the  bed  of  the  river,  a  transverse  crack  extending  from 
top  of  caisson  to  below  the  river  bed  occurred  near  the  mid  length, 
probably  due  to  tension  in  the  top  of  the  caisson  caused  by  unequal 
dredging.  This  caisson  was  unreinforced.  It  was  blasted  out  and 
replaced  by  one  reinforced  by  longitudinal  bars. 

ART.   57.     PNEUMATIC   CAISSONS 

205.  The  Compressed-air  Method. — A  pneumatic  caisson  as 
ordinarily  employed  consists  essentially  of  an  air-tight  box,  or  working 
chamber,  open  at  the  bottom,  which  may  be  filled  with  compressed 
air  to  keep  back  the  water  and  permit  the  excavation  of  the  soil  from 
below  the  bottom  of  the  caisson  by  men  working  in  the  compressed 
air.  The  working  chamber  is  ordinarily  at  the  bottom  of  a  crib, 
constructed  in  a  manner  similar  to  an  open  caisson  and  arranged  to 
be  filled  with  concrete  to  aid  in  sinking.  Shafts  with  air  locks  connect 
the  working  chamber  with  the  outside  air,  and  provide  means  of 
entering  the  working  chamber  and  transporting  materials  to  and 
from  it. 

This  method  is  frequently  employed  for  foundations  to  depths 
within  which  men  may  safely  work  in  the  compressed  air,  about  110 
feet  below  water  surface,  and  is  sometimes  combined  with  the  open- 
caisson  method,  being  used  where  obstructions  may  be  met  in  sinking 
the  open  caisson,  or  for  bedding  a  caisson  which  has  been  sunk  by 
open  dredging.  The  caissons  are  constructed  of  timber,  metal,  or 
concrete.  The  use  of  timber  caissons  has  been  quite  common  in  the 
United  States,  although  concrete  seems  to  be  coming  into  more 
general  use,  while  in  Europe,  iron  and  steel  are  preferred. 

The  pneumatic  system  was  first  applied  to  large  foundations  in 
1  Engineering  News,  Oct.  17,  1912. 


388  FOUNDATIONS 

this  country  by  Mr.  Eads  in  the  construction  of  the  St.  Louis  arch 
bridge  over  the  Mississippi  in  1870,  where  a  depth  of  109  feet  below 
water  surface  was  reached.  This  was  followed  by  the  Brooklyn 
bridge  foundations,  in  which  the  caissons  were  very  large  in  plan 
and  sunk  to  a  depth  of  78  feet.  Since  that  time,  pneumatic  caissons 
have  been  used  in  a  large  number  of  structures,  with  rapid  improve- 
ment in  the  methods  of  handling  the  work,  and  in  preventing  inju- 
rious effects  upon  men  working  in  the  compressed  air. 

Pneumatic  caissons  have  been  quite  extensively  used  for  heavy 
building  foundations,  particularly  in  New  York  City,  where  it  has 
been  found  necessary  to  carry  the  foundations  of  high  buildings 
through  unstable  materials  to  solid  rock,  without  undermining  older 
buildings  on  more  shallow  foundations.  In  such  construction, 
separate  caissons  of  small  area  are  sunk  for  individual  piers,  although 
frequently  two  or  more  piers  rest  upon  a  single  caisson.  The  layout  of 
a  foundation  for  a  heavy  building  is  a  matter  requiring  very  careful 
study.  The  first  instance  in  which  this  method  was  applied  to  a 
building  in  New  York  was  in  the  Manhattan  Life  Insurance  Com- 
pany's building  by  Kimball  &  Thompson,  architects,  in  1893.1 
Since  that  time  the  use  of  pneumatic  caissons  has  become  quite 
common. 

206.  Construction  of  Caissons. — The  materials  and  methods  of 
construction  of  a  caisson  usually  vary  with  its  size  and  shape.  Cylin- 
der caissons  are  generally  of  steel,  although  concrete  is  now  being  used 
to  considerable  extent.  The  thickness  required  for  the  concrete  walls 
usually  prevent  its  use  for  cylinders  less  than  about  8  feet  in  diameter. 
Large  caissons  of  rectangular  shape  are  frequently  made  of  timber, 
although  steel  is  sometimes  used,  while  the  use  of  concrete  is  increas- 
ing rapidly. 

The  working  chamber  is  surrounded  by  sloping  sides,  resting  upon 
the  cutting  edges  and  widening  to  give  support  to  the  roof,  which  must 
be  capable  of  carrying  the  load  of  filling  used  in  sinking  the  caisson. 
In  large  caissons  it  is  necessary  to  brace  the  side  walls,  bulkheads  being 
sometimes  built  both  transversely  and  longitudinally  across  the  work- 
ing chamber  for  the  purpose.  In  some  of  the  older  caissons,  when  the 
masonry -of  the  pier  was  built  upon  the  roof  of  the  working  chamber, 
the  roofs  were  made  very  thick.  The  roof  of  the  large  caisson  for  the 
Brooklyn  bridge  was  22  feet  thick  of  solid  timber;  that  of  the  Havre 
de  Grace  bridge  was  8  feet  thick.  In  others,  heavy  bulkheads  were 
used  to  support  thinner  roofs. 

In  timber  caissons,  in  addition  to  the  walls  of  solid  timber,  plank 
1  Engineering  Record,  Jan.  20,  1893. 


PNEUMATIC   CAISSONS  389 

sheeting  is  used  on  both  inside  and  outside  surfaces,  being  caulked 
carefully  to  make  them  air-  and  water-tight.  In  metal  caissons,  also, 
the  joints  must  be  carefully  leaded  and  caulked  to  withstand  the 
interior  air  pressure  and  outside  water  pressure.  When  the  con- 
struction above  the  roof  is  of  concrete,  reinforcement  near  the  bottom 
of  the  concrete  may  make  it  practically  self-supporting,  and  the 
roof  needs  only  sufficient  strength  to  carry  the  concrete  until  it  has 
hardened.  The  concrete  may  also  be  expected  to  exclude  the  water 
more  effectively  than  caulking. 

The  roofs  of  the  caissons  for  the  Municipal  bridge  over  the  Miss- 
issippi at  St.  Louis  consisted  of  a  single  layer  of  12-inch  timbers 
with  sheeting  of  3-inch  planks,  on  both  upper  and  lower  surfaces, 
placed  diagonally  and  well  caulked.  This  acted  as  a  form  for  the 
concrete  rilling,  which  was  reinforced  near  the  lower  surface  with 
1-inch  bars,  6  inches  apart  both  longitudinally  and  transversely.1 

In  small  caissons  for  foundations  of  buildings,  temporary  roofs 
are  sometimes  employed,  which  serve  as  forms  for  the  concrete  filling, 
and  are  removed  before  the  working  chamber  is  rilled  with  concrete, 
in  order  to  make  the  construction  monolithic,  with  no  separation 
between  the  bottom  concrete  and  the  filling. 

In  deep  caissons,  timber  cribs  are  frequently  used  upon  top  of 
the  working  chamber,  being  made  with  solid  end  and  side  walls, 
braced  with  cross  walls  or  timbers.  Such  cribs  are  usually  filled 
with  concrete,  but  in  some  instances  they  are  built  to  carry  the  whole 
load  of  the  superstructure,  and  filling  is  omitted  in  order  to  reduce 
the  weight  upon  the  foundation.  As  they  must  not  extend  above  low 
water,  cofferdams  are  required  on  top  of  the  crib  within  which  to 
build  the  masonry  piers. 

The  shafts  connecting  the  working  chambers  with  the  tops  of  the 
caissons  are  steel  cylinders.  When  the  caisson  is  of  sufficient  size 
separate  shafts  are  used  for  men  and  materials.  For  moderate 
depths,  where  ladders  are  used  by  the  men,  the  shaft  is  about  3  feet 
in  diameter,  but  when  elevators  are  employed,  it  is  made  larger. 
Shafts  for  transporting  materials  are  generally  about  2  feet  in  diam- 
eter, the  shaft  casings  frequently  being  made  so  that  they  may  be 
removed  before  the  shaft  is  filled  with  concrete,  thus  eliminating  the 
separation  between  the  concrete  used  for  filling  the  shaft  and  that  in 
the  shell  outside  and  making  a  practically  monolithic  job  when  the 
working  chamber  has  a  concrete  roof.2 

In  small  caissons  of  moderate  depth,  the  air-locks  are  placed  at 

1  Engineering  Record,  October  15,  1910. 

2  Trans.  Am.  Soc.  Civil  Engineers,  Vol.  LXI,  p.  211. 


390  FOUNDATIONS 

the  top  of  the  shafts,  while  in  large  and  deep  caissons,  they  may  be 
near  the  bottom,  but  far  enough  above  the  working  chamber  to 
provide  a  refuge  for  the  men  in  case  of  accident  at  the  bottom.  The 
lock  is  simply  a  small  room  with  two  doors,  one  leading  into  the  out- 
side air,  the  other  into  the  compressed-air  shaft,  connected  with  the 
working  chamber.  The  doors  are  arranged  to  be  held  tightly  closed 
when  the  air  pressure  is  unequal  on  their  two  sides.  In  passing 
through  the  lock,  the  men  enter  the  lock  by  the  upper  door,  which  is 
then  closed  and  the  air  pressure  in  the  lock  is  gradually  raised  to  that 
in  the  working  chamber,  after  which  the  lower  door  is  opened  and 
the  men  pass  into  the  lower  shaft  and  working  chamber. 

207.  Sinking  the  Caissons. — The  method  of  constructing  and 
placing  a  caisson  must  always  be  determined  by  local  conditions. 
When  the  caisson  is  to  be  sunk  through  a  considerable  depth  of  water, 
it  may  be  constructed  on  ways  built  on  land  and  floated  to  the  site 
where  it  is  to  be  sunk,  and  if  no  suitable  location  is  at  hand  on  shore, 
it  may  be  built  on  barges  or  pontoons,  from  which  it  can  be  launched 
or  lowered  into  position.  In  shoal  water,  a  platform  on  piles  is  some- 
times built  at  or  around  the  site,  upon  which  the  caisson  may  be  erected 
and  from  which  it  may  be  placed  in  position.  The  working  chamber 
is  built  and  made  air-tight,  then  a  sufficient  height  of  crib  or  coffer- 
dam added  to  reach  above  the  water  when  the  caisson  is  grounded  in 
the  position  in  which  it  is  to  be  sunk.  It  is  then  built  up  as  the  sink- 
ing progresses  so  as  to  keep  the  top  above  water. 

For  the  foundations  of  buildings,  the  sinking  of  the  caissons  is 
started  in  open  excavation  at  about  the  level  of  ground  water.  The 
working  chambers  when  of  small  size  are  constructed  at  a  bridge  shop 
or  a  wood-working  shop  and  hauled  to  the  site  of  the  building,  and 
are  then  set  up  in  position  and  a  section  of  concrete  shell  constructed 
on  top.  The  air  locks  are  then  placed  and  the  sinking  proceeds.  In 
some  instances,  the  whole  caisson  is  built  and  filled  with  concrete 
to  the  top  before  sinking  begins.  As  a  rule,  however,  they  are  built 
in  two  or  three  sections  heights  of  30  or  40  feet  being  sunk  at  once. 
When  the  working  chamber  is  of  concrete,  it  is  built  in  position  for 
sinking  upon  cutting  edges  previously  placed  and  held  in  position  by 
the  concrete  forms. 

In  large  caissons  sunk  through  water,  the  concrete  in  the  cribs 
provides  sufficient  weight  to  cause  sinking  to  take  place  as  the  material 
is  removed  from  beneath  the  caisson,  without  the  use  of  temporaiy 
loadings.  Sometimes  water  jets  are  used  to  reduce  friction  upon  the 
sides.  As  in  the  smaller  caissons  used  in  building  foundations, 
temporary  loadings — frequently  pig  iron — are  required  to  force  the 


PNEUMATIC   CAISSONS  391 

caissons  down,  some  means  for  handling  such  loadings  easily  must 
be  provided.  It  is  common  practice  to  employ  derricks,  which 
handle  the  loads  in  blocks  weighing  2000  to  5000  pounds,  100  to  500 
tons  total  weight  being  generally  needed. 

Excavated  material  is  removed  from  the  working  chamber  in 
buckets  through  small  shafts  with  special  air-locks  near  the  top. 
The  buckets  are  usually  operated  by  hoisting  engines  outside  the 
shaft,  but  sometimes  compressed-air  cylinders  in  the  shaft  are  used 
for  the  purpose.  In  the  caissons  for  the  Brooklyn  Bridge  foundations, 
an  open  shaft  extended  through  the  caisson  into  a  sump  below  the 
bottom  of  the  working  chamber,  the  sump  being  filled  with  water  to 
a  height  sufficient  to  balance  the  air  pressure,  the  material  being 
removed  by  dredging  through  this  shaft,  and  thrown  into  the  sump 
by  the  men  in  the  working  chamber. 

The  blow-out  or  sand-lift  method  may  be  used  in  the  removal  of 
sand  or  mud.  It  consists  in  blowing  the  material  through  a  pipe  by 
the  use  of  the  air  pressure  in  the  working  chamber.  An  open  pipe 
4  or  5  inches  in  diameter  leads  upward  from  the  working  chamber 
with  a  valve  near  its  lower  end.  The  material  is  heaped  about  the 
lower  end  of  the  pipe  and  the  valve  opened,  thus  blowing  the  mud  and 
sand  out  through  the  pipe — a  method  that  has  been  found  quite  satis- 
factory in  many  instances.  The  pipe  wears  rapidly  on  account  of 
the  high  velocity  of  the  sand  passing  through  it,  and  it  is  sometimes 
difficult  to  prevent  fluctuations  in  the  air  pressure  in  the  working 
chamber  due  to  the  amount  of  air  suddenly  withdrawn. 

The  mud  pump  is  used  for  driving  the  sand  and  mud  upward 
through  a  pipe  by  means  of  a  stream  of  water  under  pressure.  This 
method  was  first  used  by  Mr.  Eads  in  the  caissons  for  the  St.  Louis 
arch  bridge.  The  suction  of  the  pump  is  placed  in  a  sump  which  is 
kept  filled  with  water  at  the  bottom  of  the  working  chamber,  and  the 
material  to  be  removed  is  shoveled  into  the  sump  by  the  men. 

208.  Physiological  Effects  of  Compressed  Air. — The  depths  below 
water  surface  to  which  the  pneumatic  method  may  be  employed  is 
dependent  upon  the  ability  of  men  to  work  in  compressed  air.  Ex- 
perience has  shown  that  under  careful  management,  men  in  good 
physical  condition  may  safely  be  subjected  to  an  air  pressure  of 
about  45  or  50  pounds  above  atmospheric  pressure,  and  work  has  been 
successfully  carried  out  in  several  instances  at  maximum  depths  of 
110  to  115  feet  below  water  surface.  Very  careful  attention  to  the 
physical  condition  of  the  men  and  to  the  methods  used  in  entering 
and  leaving  the  compressed  air  are  necessary  to  prevent  injurious 
results. 


392  FOUNDATIONS 

When  the  men  enter  the  air  locks  and  the  air  pressure  is  gradually 
increased,  a  sensation  of  giddiness,  with  pain  in  the  ears  and  oppres- 
sive heat  is  felt.  When  equilibrium  between  the  air  pressures  outside 
and  inside  the  body  has  been  reached,  a  feeling  of  exhilaration  results 
while  breathing  the  more  dense  air.  Labor  in  the  compressed  air  is 
more  exhausting  than  in  the  outside  air,  and  is  carried  on  in  shorter 
shifts.  As  the  pressure  is  reduced,  on  leaving  the  caisson,  a  sensation 
of  intense  cold  is  experienced,  accompanied  by  an  itching  feeling  under 
the  skin.  Warm  clothing  is  necessary,  and  it  is  customary  to  serve  hot 
coffee  to  the  men  as  they  leave  the  locks.  These  are  the  usual  and 
normal  sensations  experienced  by  those  working  in  compressed  air. 
The  effects  are  greater  the  first  time  the  air  is  encountered,  and  the 
unpleasant  sensations  are  gradually  eliminated  as  experience  teaches 
the  proper  method  of  meeting  them. 

Caisson  disease  is  a  malady  which  sometimes  results  from  working 
in  compressed  air  and  develops  severe  pains  in  the  joints,  resembling 
rheumatism,  causing  the  patient  to  double  up,  and  is  commonly 
known  as  the  "bends."  It  is  experienced  only  after  returning  to 
atmospheric  pressure,  and  is  sometimes  relieved  by  returning  to  the 
compressed  air  and  coming  out  again  very  slowly,  medical  locks  being 
sometimes  provided  for  this  purpose.  In  many  instances  the  patient 
is  partially  paralyzed,  and  when  the  attack  is  severe  a  long  time  may 
be  required  for  recovery.  In  the  most  serious  cases,  congestion  of  the 
brain  and  sometimes  death  may  result. 

Much  has  been  learned  through  experience  concerning  the  methods 
of  preventing  and  treating  caisson  disease  since  the  pneumatic  proc- 
ess has  been  in  use.  In  sinking  the  caissons  of  the  St.  Louis  bridge, 
119  cases  of  caisson  disease  developed  and  14  deaths  occurred.  The 
better  control  in  later  work  has  largely  eliminated  this  danger,  but 
failure  to  exercise  sufficient  care,  or  unforeseen  contingencies,  still 
frequently  cause  trouble  from  this  source. 

The  rate  of  decompression  in  coming  out  of  the  compressed  air  is 
a  matter  of  importance,  and  the  time  allowed  is  not  usually  sufficient, 
according  to  the  opinions  of  most  medical  authorities,  to  insure  safety. 
The  length  of  working  shift  should  be  reduced  as  the  pressure  increases 
The  proper  ventilation  of  the  working  chamber  is  of  greater  impor- 
tance than  for  men  working  at  atmospheric  pressure,  and  arrange- 
ments must  be  made  for  frequent  changes  of  air. 


BRIDGE  PIERS  AND  ABUTMENTS  393 


ART.   58.     BRIDGE   PIERS   AND   ABUTMENTS 

209.  Locations  and  Dimensions  for  Piers. — In  fixing  the  locations 
for  piers  of  a  bridge,  there  are  a  number  of  factors  which  it  may  be 
necessary  to  take  into  consideration.  In  a  navigable  stream,  they 
must  be  arranged  so  as  to  obstruct  the  channel  as  little  as  possible 
and  meet  the  regulations  imposed  by  the  Government.  This  may 
simetimes  determine  positions,  length  of  span,  and  height  of  structure. 
The  waterway  requirements  and  possibility  of  the  piers  restricting 
the  waterway  to  a  serious  extent  must  always  be  considered.  The 
character  of  the  foundation  along  the  line  of  the  bridge,  and  probable 
difficulty  of  placing  foundations  at  various  locations  may  sometimes 
influence  the  choice  of  positions  for  piers. 

Financial  considerations  are  always  important.  The  total  cost  of 
the  structure  including  piers  and  superstructure  should  be  the  mini- 
mum consistent  with  properly  meeting  the  other  requirements.  The 
cost  of  superstructure  increases  approximately  as  the  square  of  the 
length  of  span,  while  the  cost  of  piers  may  be  nearly  proportional  to 
their  number.  An  arrangement  may  therefore  be  worked  out  in 
each  instance  which  will  give  a  minimum  of  cost  for  the  entire 
structure. 

Aesthetic  considerations  may  also  have  an  influence  on  pier  loca- 
tion; the  appearance  of  the  structure  is  always  an  important  matter 
and  may  sometimes  control  the  design.  The  arrangement  of  spans 
to  secure  symmetry  in  the  whole  structure,  with  proper  placing  of 
dominating  features  ought  to  be  carefully  considered. 

The  shape  to  be  given  to  a  pier  is  determined  by  the  requirements 
of  each  particular  case.  It  must  be  designed  safely  to  transmit  to 
the  foundation,  the  loads  brought  upon  it,  and  to  resist  any  lateral 
pressure  due  to  wind  or  current,  and  the  form  to  be  given  a  horizontal 
section  should  offer  as  little  resistance  as  possible  to  the  flow  of  the 
stream  in  which  it  may  be  placed. 

The  most  common  form  for  piers  in  streams  is  that  of  a  rectangle 
of  length  a  little  more  than  the  width  of  the  bridge,  with  triangular 
or  curved  ends.  The  pointed  ends  below  high  water  are  known  as 
starlings,  and  are  intended  to  reduce  the  disturbance  to  the  stream 
flow  and  sometimes  to  act  as  ice  breakers.  Sometimes  starlings  are 
used  only  on  the  up-stream  end  of  the  pier,  but  more  commonly  the 
horizontal  section  is  made  symmetrical.  The  down-stream  starling 
serves  to  prevent  eddies  below  the  pier,  and  to  equalize  the  load  over 
the  foundation  area.  Starlings  are  necessary  only  below  high  water, 
and  the  upper  part  of  the  pier  is  sometimes  made  rectangular,  but 


394 


FOUNDATIONS 


more  commonly  the  ends  are  semicircular  (see  Fig.  123)  or  the  shape 
of  the  starling  is  continued  to  the  top. 


FIG.  123. 


Fig.  124  shows  a  simple  form  of  concrete  pier  in  which  a  triangular 

starling  is  used  upon  the  up- 
stream end  only  and  is  continued 
to  the  top  of  the  pier.  In  Fig. 
123  the  horizontal  section  of  the 
starling  is  composed  of  two  inter- 
secting circular  arcs  of  radius 
equal  to  the  width  of  the  pier, 
while  the  upper  part  of  the  pier 
has  semicircular  ends. 

The  dimensions  required  for 
the  top  of  a  pier  are  usually  fixed 
mainly  by  the  area  of  the  bear- 
ings needed  for  the  superstruc- 
ture. A  coping  not  less  than 
1  foot  in  thickness  is  placed  on  the  top  of  the  pier,  projecting  3  to 
6  inches  beyond  the  top  of  the  masonry  beneath.  The  dimensions  of 


FIG.  124. 


BRIDGE  PIERS  AND  ABUTMENTS  395 

the  top  of  the  pier  should  be  such  that  the  base  plate  of  the  super- 
structure shall  not  come  within  4  to  6  inches  of  the  edges  of  the 
masonry  under  the  coping.  The  width  of  the  top  of  the  pier  under 
the  coping  is  required  to  be  at  least  4  feet,  and  at  least  1  foot  more 
than  is  needed  for  the  base  plate. 

A  batter  of  at  least  J  inch  to  1  foot,  or  sometimes  1  inch  to  1 
foot,  is  given  to  the  surfaces  of  the  pier.  Footing  courses  may  be 
employed  at  the  base  of  the  pier  to  distribute  the  loads  over  a  larger 
area  of  the  foundation,  being  commonly  stepped  off,  projecting 
about  a  foot  horizontally  and  with  a  depth  about  twice  the  width. 
When  of  reinforced  concrete  the  projecting  steps  may  be  designed  as 
cantilever  slabs. 

Cylinder  piers  are  frequently  used  when  the  sectional  area  of  a 
single  solid  pier  is  not  necessary  to  stability.  These  consist  of  a  pair 
of  cylinders  arranged  so  that  each  may  carry  the  ends  of  the  trusses 
upon  one  side  of  the  bridge,  and  are  connected  by  bracing  near  the 
top  to  give  rigidity  transversely  to  the  length  of  the  bridge.  They 
are  either  thin  steel  shells  filled  with  concrete,  or  monolithic  con- 
crete shafts,  reinforced  near  the  outer  surfaces. 

210.  Stability  of  Piers. — A  masonry  pier  is  a  vertical  column  carry- 
ing both  vertical  and  transverse  loads.  The  vertical  loads  carried  by 
any  horizontal  section  of  the  pier  consist  of  the  weight  of  the  super- 
structure with  its  live  load  and  the  weight  of  the  pier  above  the 
section  considered.  The  effect  of  impact  is  not  usually  considered, 
although  a  small  allowance  for  impact  is  sometimes  added  for  the 
upper  part  of  railroad  bridge  piers. 

The  wind  and  current  pressures  are  horizontal  forces  which  tend 
to  produce  bending  moments  in  any  horizontal  section  of  the  pier, 
and  in  the  foundation,  in  a  direction  normal  to  the  bridge.  The  wind 
load  upon  the  superstructure  and  upon  a  railway  train  upon  the 
bridge  may  be  taken  the  same  as  in  designing  the  superstructure. 
Wind  upon  the  end  of  the  pier  is  commonly  taken  at  about  20  pounds 
per  square  foot  of  vertical  section  for  semicircular  ends,  but  may  be 
reduced  to  15  pounds  for  pointed  ends,  and  should  be  increased  to 
30  pounds  for  rectangular  piers. 

The  pressure  of  a  current  of  water  upon  the  end  of  a  pier  cannot 
be  accurately  determined;  in  pounds  per  square  foot  of  vertical  sec- 
tion, it  is  frequently  taken  at  about  .75v2  (where  v  is  the  surface  velo- 
city of  the  stream  in  feet  per  second)  for  curved  or  pointed  starlings 
and  about  twice  this  amount  for  rectangular  piers.  The  center  of 
pressure  is  assumed  to  be  at  one-third  the  depth  from  the  surface  to 
the  bottom  of  the  stream. 


396 


FOUNDATIONS 


7 
X 


The  pressure  exerted  by  ice  depends  upon  the  thickness  of  the  ice 
and  the  shape  of  the  up-stream  end  of  the  pier,  and  is  greatest  when 
the  ice  is  breaking  up  and  a  large  body  of  floating  ice  is  being  cut  by 
the  pier.  Where  ice  10  or  12  inches  thick  may  form,  a  pressure  of 
45,000  to  50,000  pounds  per  foot  of  width  of  pier  is  often  assumed, 
considered  as  concentrated  at  the  level  of  high  water.  For  other 
thicknesses,  the  pressure  is  somewhat  proportional  to  the  thickness. 

Where  heavy  ice  is  likely  to  form, 
the  use  of  ice  breakers,  or  starlings 
with  edges  inclined  to  the  vertical 
(as  shown  in  Fig.  125)  may 
materially  decrease  the  pressure. 
The  tractive  force  in  the  piers 
of  a  railway  bridge  is  a  horizontal 
force  acting  parallel  with  the 
length  of  the  bridge  at  the  level 
of  the  rail,  and  therefore  pro- 
duces moments  in  the  horizontal 
sections  of  the  pier  and  founda- 
tion at  right  angles  to  those  due 
to  wind  and  current.  The  trac- 
tive force  is  commonly  taken 
at  2/10  of  the  moving  load  on  one  track. 

It  is  essential  to  stability  that  the  maximum  compressive  stress 
upon  any  horizontal  section  due  to  the  vertical  loads  combined  with 
that  due  to  the  moments  of  the  horizontal  forces  shall  not  exceed  the 
safe  compressive  strength  of  the  masonry.  The  maximum  unit  pres- 
sure upon  the  foundation  must  not  exceed  a  safe  value.  No  tension 
should  exist  in  the  masonry  at  any  section  under  any  possible  loading, 
unless  it  be  reinforced  concrete  designed  for  tension,  and  compression 
must  always  exist  over  the  whole  area  of  the  foundation. 

The  horizontal  forces  must  not  be  sufficient  to  produce  sliding 
upon  any  joint  in  the  masonry  or  foundation,  or  to  shear  any  section 
of  concrete. 

Ordinary  solid  piers  dimensioned  to  give  sufficient  bearing  area 
at  the  top  and  slightly  battered  will  usually  be  amply  strong.  The 
distribution  of  loads  over  the  foundation  should,  however,  be  care- 
fully looked  after. 

Large  masonry  piers  are  frequently  built  hollow.  The  masonry 
under  the  base  plates  of  the  superstructure  is  considered  to  act  as 
columns  which  transmit  the  vertical  loads  to  the  foundation,  and  the 
central  part  of  the  pier  is  regarded  as  bracing  to  stiffen  the  columns 


FIG.  125. 


BRIDGE   PIERS  AND  ABUTMENTS 


397 


and  carry  the  lateral  loads.  A  part  of  the  masonry  at  the  center  of 
the  pier  may  be  left  out  without  appreciably  reducing  its  strength,  thus 
reducing  the  weight  upon  the  foundation  and  saving  a  considerable 
volume  of  masonry  or  concrete.  Such  an  arrangement  is  shown  in 
Fig.  126. 

Hollow  piers  of  reinforced  concrete  have  been  occasionally  used. 
These  have  been  designed  in  a  number  of  ways,  columns  being  used 
under  the  base  plates  of  the  superstructure,  connected  in  some  way 
by  reinforced  bracing.  The  exterior  shape  of  these  piers  below  high 
water  is  made  the  same  as  solid  piers  in  order  to  produce  minimum 
disturbance  of  stream  flow. 

-  The  pier  below  high  water  is  hollow,  with  reinforced  side  walls 
connecting  the  towers  at  the  ends.     Above  high  water,  the  towers 


FIG.  126. 

are  separate  and  connected  by  a  reinforced  arch  at  the  top.  Openings 
are  provided  through  the  walls  to  admit  water  to  the  interior  spaces. 

211.  Construction  of  Piers. — Solid  bridge  piers  are  constructed  of 
concrete  or  of  concrete  with  facing  of  cut  stone.  The  use  of  rubble 
masonry  as  backing  in  such  work  has  given  way  to  concrete  on  ac- 
count of  its  less  cost  and  greater  ease  of  handling. 

Stone  masonry  facing  has  the  advantage  of  presenting  a  pleasing 
appearance,  and  offering  good  resistance  to  the  abrasion  of  the 
stream  and  of  floating  debris.  In  constructing  a  pier  by  its  use  forms 
are  unnecessary,  which  frequently  results  in  lessened  cost  of  con- 
struction, although  the  cost  of  the  masonry  itself  is  greater  than  that 
of  concrete.  First-class  ashlar  masonry  is  required  in  such  work,  and 
the  stone  must  be  well  bonded  into  the  concrete  backing.  In  im- 
portant work  carrying  heavy  loadings,  the  facing  stones  are  tied  to 


398  FOUNDATIONS 

the  concrete  by  the  use  of  steel  rods  attached  to  the  stretchers  at 
frequent  intervals  and  extending  well  into  the  concrete. 

When  piers  are  wholly  of  concrete,  it  is  desirable  to  place  light 
reinforcement  near  the  surface  in  the  face  of  the  pier  to  prevent 
surface  cracks,  which  usually  develop  in  any  large  exposed  surface  of 
concrete.  This  would  require  horizontal  bars  not  more  than  1  foot 
apart,  and  vertical  bars  every  2  or  3  feet,  embedded  about  2  inches  in 
the  concrete.  The  top  of  the  coping  should  be  similarly  reinforced. 

Cylinder  piers  are  most  commonly  formed  by  constructing  a 
cylindrical  shell  of  steel  and  filling  it  with  concrete.  Reinforced 
concrete  cylinders  are  also  coming  into  use,  and  have  the  advantage 
of  not  requiring  painting  to  prevent  rust.  A  pair  of  cylinders  is  gen- 
erally used  for  a  pier  and  they  are  connected  by  bracing  near  the  top 
or  at  two  points  for  high  piers.  This  bracing  may  be  of  reinforced 
concrete,  or  sometimes  a  steel  truss  inclosed  in  concrete. 

The  masonry  of  a  pier  may  be  supported  upon  a  caisson,  or  upon 
hard  material  or  piles  in  a  cofferdam.  When  the  pier  rests  upon  a 
caisson,  a  cofferdam  is  built  upon  the  top  of  the  caisson  and  the 
masonry  built  inside  the  cofferdam  after  filling  the  caisson  with  con- 
crete. When  the  pier  rests  upon  piles,  the  tops  of  the  piles  extend 
upward  into  and  are  inclosed  by  the  concrete  in  the  base  of  the  pier. 
In  such  work,  it  is  desirable  to  place  reinforcement  in  the  bottom  of 
the  footing  of  the  pier  between  the  piles. 

212.  Types  of  Bridge  Abutments. — A  bridge  abutment  is  a  com- 
bination of  a  pier  with  a  retaining  wall;  it  carries  the  weight  of  one 
end  of  the  bridge  with  its  moving  load  and  retains  the  bank  of  earth 
sustaining  the  roadway  leading  to  the  bridge,  the  requirements  for 
stability  being  the  same  as  those  for  a  retaining  wall.  The  weight 
of  the  bridge  with  its  live  load  is  brought  upon  the  abutment  near 
the  top,  and  the  thrust  of  the  earth  filling  with  that  of  the  load  upon 
the  roadway  is  brought  upon  the  back  of  the  abutment,  as  shown  in 
Fig.  127.  These,  with  the  weight  of  the  pier  itself,  must  give  a 
proper  distribution  of  pressures  upon  the  foundation  and  safe  stresses 
at  any  point  in  the  masonry. 

The  filling  supporting  the  roadway  usually  has  side  slopes  about 
1.5  horizontal  to  1  vertical,  which  must  be  sustained  by  walls  joined 
to  the  abutments.  Abutments  are  divided  according  to  the  method 
used  for  supporting  the  side  slopes  into  straight  abutments,  wing 
abutments,  U  abutments,  and  T  abutments. 

Straight  abutments  are  those  in  which  the  walls  retaining  the  side 
slopes  are  continuations  of  the  abutments  in  the  same  lines,  as  shown 
in  Fig.  127. 


BRIDGE  PIERS  AND  ABUTMENTS 


399 


Wing  abutments  are  those  in  which  the  side  slopes  are  retained 
by  wing  walls,  making  an  angle,  usually  about  30°  with  the  face  of  the 
abutment  (see  Fig.  128).  This  type  of  abutment  is  selected  where  a 


Side  Elevation 


FIG.  127. — Straight  Abutment. 

stream  flows  past  the  face  of  the  abutment,  as  it  disturbs  the  flow  of 
the  stream  to  the  least  extent  and  protects  the  abutment  against  the 
stream  getting  behind  it.  The  wing  walls  may  be  shorter  and  require 

~~~          \ 


a 


B 


*ia.  128. 

somewhat  less  masonry  then  the  walls  of  straight  abutments,  when 
the  bottom  of  the  sloping  earth  is  held  back  to  the  line  of  the  face  of 
the  abutment. 


400 


FOUNDATIONS 


M-Abutments  are  those  in  which  the  walls  are  turned  at  right  an- 
_______ gles  to  the  abut- 
ment as  shown  in 
Fig.  129.  The 
earth  slope  is  then 
upon  the  face  of 
the  wall.  They 
may.  be  economical 
when  the  abut- 
ment is  on  the  edge 

of  a  bluff  so  that  the  depth  of  the  wall  may 
be  reduced  by  running  into  the  face  of  the 
bluff. 

Foundations  of  Bridges  and  Buildings  by 
Jacoby  and  Davis,  New  York,  1914,  gives  a 
complete  description  of  the  various  methods  of  constructing  founda- 
tions, with  detailed  descriptions  of  many  important  constructions. 


-  E/evation 
FIG.  129. 


INDEX 


Abutments,  types  of,  398 
— ,  U-,  400 
— ,  wing,  399 
Aggregates,  kinds  of,  111 
— ,  mechanical  analysis  of,  112,  118 
— ,  measuring  fine,  40 
— ,  selection  of,  115 
— ,  specific  gravity,  113 
— ,  specifications  for,  39 
— ,  tests  for,  113 
— ,  voids  in,  114 

American  Railway  Engineering  Asso- 
ciation, 69,  76,  362 
Arches,  elastic,  295,  302 
— ,  analysis  of,  314,  317,  334 
— ,  effect  of  direct  thrust,  299 
— ,  temperature  effects,  299 
— ,  theory  of,  295 
Arches,  hinged,  310 
— ,  reinforced,  see  Reinforced  concrete 

arches 

— ,  Roman,  5 
— ,  unsymmetrical,  311 
— ,  voussoir,  abutments  for,  291 
— ,  — ,  earth  pressures  on,  288 
— ,  — ,  line  of  pressure  in,  284,  292 
— ,  — ,  loads  for,  286 
— ,  — ,  parts  of,  282 
— ,  — ,  stability  of,  283,  291 
— ,  — ,  thickness  for,  289 
—  with  elastic  piers,  312 
Ashlar  masonry,  70,  73 

,  strength  of,  79 

,  weight  of,  80 

Assyrian  architecture,  3,  4 

Beams,  reinforced  concrete,  see  Rein- 
forced concrete  beams 


Bond  strength  of  reinforced  concrete, 

154,  173, 177, 186 
Brick,  definition,  1 

—  masonry,  bond  in,  94 
— ,  cost  of,  100 

,  efflorescence  in,  99 

,  hollow  walls,  97 

,  joints  in,  93 

—  — ,  laying,  94 

,  measurement  of,  100 

—  — ,  mortar  for,  94,  101 
— •  — ,  strength  of,  97 

—  — ,  uses  of,  2 

Bricks,  clay  and  shale,  84-88 

— ,  classification  of,  87 

— ,  clay  for,  86 

— ,  composition  of,  85 

— ,  pressed,  87 

— ,  vitrified,  88 

— ,  sand-lime,  88-90 

— ,  — ,  caustic  lime  process,  89 

— ,  — ,  hydrated  line  process,  89 

— ,  — ,  properties  of,  90 

— ,  sizes  of,  92 

— ,  — ,  sun-dried,  3 

— ,  tests  for,  91 

Bridge  piers,  construction  of,  397 

,  dimensions  for,  393 

,  hollow,  397 

,  stability  of,  395 

Bridges,  concrete,  girder,  278 
— ,  — ,  loading  for,  271 
— ,  — ,  slab,  273 
— ,  — ,  T-beam,  275 
Building  stone,  51-60 

,  classification,  52 

,  fire  resistance,  60 

— ,  seasoning,  61 
401 


402 


INDEX 


Building  stone,  strength  of,  59 
— ,  temperature  effects,  59 
,  tests  for,  61 

Caissons,  box,  376 

— ,  cylinder,  380 

— ,  dredging  through  wells,  383 

— ,  open,  377 

— ,  pneumatic,  387 

— ,  steel,  385 

— ,  timber,  378,  384 

Cantilever  foundations,  375 

Cement,  hardening  of,  16 

— ,  history  of,  6 

— ,  hydraulic,  definition,  10 

— ,  mixed,  21 

— ,  natural,  20 

— ,  permanence  of  volume,  23 

— ,  Portland,  see  Portland  cement 

— ,  puzzohm.  21 

— ,  Roman,  20 

— ,  setting  of,  16 

— ,  silica,  22 

—  slag,  21 

— ,  specifications  of  1916,  27 

Cement,  Tests  for,  accelerated,  29 

— , ,  adhesive  strength,  31 

— , ,  compressive  strength,  30 

— , ,  standard,  27 

— , ,  soundness,  29 

— , ,  transverse  strength,  30 

Cement  mortar,  materials  required,  44 
,  mixing,  42 

— ,  proportioning,  39 

,  retempering,  43 

,  sand  for,  31 

,  strength  of,  45 

—  yield  of,  44 
Chaldean  construction,  3 
Chenoweth  piles,  370 
Clay  bricks,  see  Bricks,  clay  and  shale 
Cofferdams,  crib,  380 
— ,  earth,  378 
— ,  sheet-pile,  379 
Columns,  concrete,  206 
— ,  eccentric  loads  on,  212 
— ,  examples  in,  208,  211 
— ,  hooped  reinforcement,  209 
— ,  longitudinal  reinforcement,  207 
Compressed  air,  caisson  disease,  392 
, ,  physiological  effects,  391 


Concrete,  cost  of,  149 

— ,  consistency  of,  130,  146 

— ,  contraction  joints,  133 

Concrete  culverts,  326,  329,  331 

— ,  durability  of,  140. 

— ,  density  of,  144,  146 

— ,  expansion  and  contraction  of,  133 

— ,  fire  resistance  of,  143 

—  foundations,  352 

,  design  of,  354 

— ,  freezing  of,  131 

—  materials  required  for,  123 

—  mechanical  analysis  curve,  118 

—  mixers,  128 

—  mixing,  125 

— ,  permeability  of,  136 

—  piles,  367 
— ,  placing,  130 

— ,  proportioning,  116 

— ,  reinforced,  see  Reinforced  concrete 

—  rubble,  269 

—  surfaces,  finishing,  135 
— ,  strength  of,  144 

— ,  transportation  of,  129 

— ,  waterproofing,  137 

Conduits,  analysis  of  gravity,  334 

— ,  earth  pressures  on,  333 

— ,  stresses  in,  338 

Construction,  Assyrian,  4 

— ,  Chaldean,  3 

— ,  Egyptian,  4 

Copings,  72,  75 

Costs  of  brick  masonry,  100 

concrete,  149 

stone  masonry,  83 

Coulomb's  theory  of  earth  pressure,  214 

Culverts,  arch,  331 

— ,  box,  327,  329 

— ,  pipe,  see  Pipe  culvert 

— ,  types  of,  321 

— ,  waterway  area,  321 

Dams,  arched,  259-266 

— ,  —  constant  angled,  262 

— ,  —  horizontal  shear  in,  261 

— ,  —  temperature  stresses  in,  263 

— ,  construction  of,  268 

— ,  gravity,  curved,  258 

— ,  — ,  design  of  profile  for,  251 

— ,  — ,  distribution  of  pressures,  255 

— ,  — ,  graphical  analysis  of,  249 


INDEX 


403 


Dams,  gravity,  horizontal  tensions  in, 

256 

— ,  — ,  ice  pressures  on,  253 
— ,  — ,  stability  of,  247 
— ,  — ,  uplift  in,  253 
— ,  masonry  for,  269 
— ,  multiple  arched,  263 
— ,  overflow,  269 
— ,  reinforced  concrete,  266 

Earth  pressures,  angle  of  friction,  220 

,  computation  of,  218 

,  graphical  method  for,  221 

—  — ,  table  of,  219 
— ,  theories  of,  214 

Efflorescence  in  brick  walls,  99 
Egyptian  construction,  4 
Equilibrium  polygon,  294 
Expansion    and    contraction    of    con- 
crete, 133 

Fire  resistance  of  concrete,  143 

Foundations,  cantilever,  357 

— ,  pile,  see  Pile  foundations 

— ,  pneumatic,  caissons,  see  Caissons 

— ,  — ,  compressed  air,  391 

— ,  — ,  sinking,  390 

— ,  soils,  see  Soils 

— ,  spread,  347 

,  concrete,  352 

— ,  — ,  grillage,  349,  352 
— ,  — ,  masonry,  348 
— ,  — ,  steel,  350 
Freezing  of  concrete,  131 
Frost  batter  in  walls,  246 

Gneiss,  53 

Granite,  52 

— ,  durability  of,  60 

— ,  strength  of,  59 

Grillage  foundations,  349,  352 

Gypsum  blocks,  107 

—  plasters,  48 

Hollow  clay  blocks,  see  Structural  tiling 
Hydrated  lime,  15,  94,  138 
Hydraulic  index,  13 

Influence  lines,  314 
Keene's  cement,  49 


Lime,  common,  9,  11 
— ,  hydraulic,  11,  13 
— ,  hydrated,  15,  94,  138 
— ,  putty,  15 
Limestone,  53 
— ,  durability  of,  60 
— ,  strength  of,  58 
Loads  for  bridges,  271 
—  arches,  286,  300 

Marble,  54 

— ,  strength  of,  59 

Masonry,  brick,  see  Brick  masonry 

— ,  cyclopean,  269 

— ,  rubble  concrete,  269 

— ,  stone,  see  Stone  masonry 

Mortar,  cement,  see  Cement  mortar 

Piers,  bridge,  see  Bridge  piers 

Pile-drivers,  359 

Piles,  bearing  power,  364 

-  classification  of,  358 
— ,  concrete,  367 
— ,  pedestal,  368 
— ,  sand,  359 
— ,  sheet,  371 
— ,  timber,  362 
Pipe  culverts,  cast  iron,  325 

— ,  concrete,  326 
and  walls,  325 

— ,  vitrified,  324 
Plasters,  gypsum,  48 
— ,  hard  finish,  50 
Portland  cement,  18 

— ,  burning,  19 

— ,  composition,  19,  24 

— ,  silica  ratio,  26 
Proportioning  concrete,  116 

-  by  trial,  120 
—  — ,  fineness  modulus,  121 
Puzzolan  cement,  21 
Pyrobar  floor  tile,  108 

Quicklime,  12 

Rankine's  theory  of  earth  pressure,  216 
Raymond  concrete  pile,  367 
Reinforced  concrete,  arches,  analysis  of, 
302,  314,  317 

— ,  —  division  of  arch  ring,  301,  317 

— ,  —  design  of,  300 


404 


INDEX 


Reinforced  concrete,  arches,  loads  for, 

300 

— ,  —  stresses  in,  305 
— i  —  types  of,  309 
Reinforced  concrete  beams,   compres- 
sion reinforcement,  186 

,  design  of,  176 

,  diagonal  tension  in,  168,  178 

— ,  flexure  formulas,  158,  179,  186 
— ,  shear  in,  167,  177,  182 

,  spacing  of  steel,  173 

,  tables  for,  162,  188 

— ,  T-beams,  179,  183,  198 
Reinforced    concrete,    bond    strength, 

154,  173 

— ,  columns,  206 
— ,  history  of,  7 

,  modulus  of  elasticity,  156 

Retaining  walls,   concrete,   cantilever, 

229,  231 

— ,  — ,  counterforted,  230,  238 
— ,  — ,  design  of,  230,  238 
— ,  — ,  examples  of,  231,  235,  238 
— ,  Baker's  rules,  221 

,  earth  pressure  upon,  214 

,  empirical  design,  225 

,  foundations  for,  244 

,  graphical  method,  221 

— ,  stability  of,  223 

,  surcharged,  221,  238 

,  Trautwine's  rules,  225 

Roman  arches,  5 
Rubble  masonry,  71 
— ,  strength  of,  79 
— ,  weight  of,  80 

Sand  for  mortar,  31 

— ,  density  of,  37 

— ,  specifications  for,  39 

— ,  tests  for,  34 

Sandstone,  54 

— ,  durability  of,  55,  60 


Sandstone,  strength  of,  58,  59 

Sea  water,  action  on  concrete,  141 

Setting  of  cement,  16 

Sheet-piling,  371 

Simplex  concrete  piles,  367 

Slab  and  buttress  dams,  267 

Slabs,  reinforced  concrete,  194 

Soils,  bearing  capacity,  344,  346 

— ,  examination  of,  342 

— ,  tests  for,  345 

Steel  for  reinforced  concrete,  155 

— ,  bond  strength  of,  173,  177 

— ,  tables  for,  166,  199 

Stone  building,  see  Building  stone 

—  cutting,  62-70 

—  masonry,  1,  70-84 
— ,  ashlar,  70,  73 

,  bearing  blocks,  80 

— ,  capstones,  80 

— ,  cost  of,  82 

— ,  corbels,  82 

— ,  strength  of,  78 
Structural  tiling,  102 

— ,  wall  construction,  105 
Syenite,  53 

T-beam  bridges,  275 
T-beams,  see  Reinforced  concrete  beams 
Tests  for  aggregates,  113 
—  bricks,  91 

cements,  27 

concrete,  147 

Voussoir  arches,  see  Arches,  voussoir 

Walls  of  stone  masonry,  72 
Waterproof  concrete,  137 
Water-tables,  75 
Window  sills,  76 

Yield  of  concrete,  122 


'•*": 

Wiley  Special  Subject  Catalogues 

For  convenience  a  list  of  the  Wiley  Special  Subject 
Catalogues,  envelope  size,  has  been  printed.  These 
are  arranged  in  groups — each  catalogue  having  a  key 
symbol.  (See  special  Subject  List  Below).  To 
obtain  any  of  these  catalogues,  send  a  postal  using  r 
the  key  symbols  of  the  Catalogues  desired. 

————— — — — 

1 — Agriculture.     Animal  Husbandry.     Dairying.     Industrial 
Canning  and  Preserving. 

2 — Architecture.  •    Building.      Concrete  and  Masonry. 

3 — Business  Administration  and  Management.     Law. 

Industrial  Processes:   Canning  and  Preserving;     Oil  and  Gas 
Production;  Paint;  Printing;  Sugar  Manufacture;  Textile. 

CHEMISTRY 

4a  General;  Analytical,  Qualitative  and  Quantitative;  Inorganic; 

Organic. 
4b  Electro-  and  Physical;  Food  and  Water;  Industrial;  Medical 

and  Pharmaceutical;  Sugar. 

^01 
CIVIL  ENGINEERING 

5a  Unclassified  and  Structural  Engineering. 

5b  Materials  and  Mechanics  of  Construction,  including;  Cement 
and  Concrete;  Excavation  and  Earthwork;  Foundations; 
Masonry. 

5c  Railroads;  Surveying. 

5d  Dams;  Hydraulic  Engineering;  Pumping  and  Hydraulics;  Irri- 
gation Engineering;  River  and  Harbor  Engineering;  Water 
Supply. 


noiJBIO': 


CIVIL  ENGINEERING—  Continued 

5e  Highways;  Municipal  Engineering;  Sanitary  Engineering; 
Water  Supply.  Forestry.  Horticulture,  Botany  and 
Landscape  Gardening. 


6 — Design.       Decoration.       Drawing:     General;      Descriptive 
Geometry;  Kinematics;  Mechanical. 

ELECTRICAL  ENGINEERING— PHYSICS 
7 — General  and  Unclassified;  Batteries;  Central  Station  Practice; 
Distribution  and   Transmission;  Dynamo-Electro   Machinery; 
Electro-Chemistry  and   Metallurgy;    Measuring     Instruments 
and  Miscellaneous  Apparatus. 


8 — Astronomy.      Meteorology.      Explosives.      Marine    and 
Naval  Engineering.     Military.     Miscellaneous  Books. 

MATHEMATICS 

9 — General;    Algebra;   Analytic  and   Plane   Geometry;    Calculus; 
Trigonometry;  Vector  Analysis. 

MECHANICAL  ENGINEERING 

lOa  General  and  Unclassified;  Foundry  Practice;  Shop  Practice. 
lOb  Gas  Power  and    Internal   Combustion  Engines;  Heating  and 

Ventilation;  Refrigeration. 
lOc   Machine  Design  and  Mechanism;  Power  Transmission;  Steam 

Power  and  Power  Plants;  Thermodynamics  and  Heat  Power. 
1 1 — Mechanics.  ___ 

12 — Medicine.  Pharmacy.  Medical  and  Pharmaceutical  Chem- 
istry. Sanitary  Science  and  Engineering.  Bacteriology  and 

Biology. 

MINING  ENGINEERING 

13 — General;  Assaying;  Excavation,  Earthwork,  Tunneling,  Etc.; 
Explosives;  Geology;  Metallurgy;  Mineralogy;  Prospecting^ 
Ventilation. 

14 — Food  and  Water.  Sanitation.  Landscape  Gardening. 
Design  and  Decoration.  Housing,  House  Painting. 


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